The Hubble Constant
 4.8k Downloads
 10 Citations
Abstract
I review the current state of determinations of the Hubble constant, which gives the length scale of the Universe by relating the expansion velocity of objects to their distance. There are two broad categories of measurements. The first uses individual astrophysical objects which have some property that allows their intrinsic luminosity or size to be determined, or allows the determination of their distance by geometric means. The second category comprises the use of allsky cosmic microwave background, or correlations between large samples of galaxies, to determine information about the geometry of the Universe and hence the Hubble constant, typically in a combination with other cosmological parameters. Many, but not all, objectbased measurements give H_{0} values of around 72–74 km s^{−1} Mpc^{−1}, with typical errors of 2–3 km s^{−1} Mpc^{−1}. This is in mild discrepancy with CMBbased measurements, in particular those from the Planck satellite, which give values of 67–68 km s^{−1} Mpc^{−1} and typical errors of 1–2 km s^{−1} Mpc^{−1}. The size of the remaining systematics indicate that accuracy rather than precision is the remaining problem in a good determination of the Hubble constant. Whether a discrepancy exists, and whether new physics is needed to resolve it, depends on details of the systematics of the objectbased methods, and also on the assumptions about other cosmological parameters and which datasets are combined in the case of the allsky methods.
Keywords
Cosmology Hubble constant1 Introduction
1.1 A brief history
The last century saw an expansion in our view of the world from a static, Galaxysized Universe, whose constituents were stars and “nebulae” of unknown but possibly stellar origin, to the view that the observable Universe is in a state of expansion from an initial singularity over ten billion years ago, and contains approximately 100 billion galaxies. This paradigm shift was summarised in a famous debate between Shapley and Curtis in 1920; summaries of the views of each protagonist can be found in [43] and [195].
The historical background to this change in world view has been extensively discussed and whole books have been devoted to the subject of distance measurement in astronomy [176]. At the heart of the change was the conclusive proof that what we now know as external galaxies lay at huge distances, much greater than those between objects in our own Galaxy. The earliest such distance determinations included those of the galaxies NGC 6822 [93], M33 [94] and M31 [96], by Edwin Hubble.
Recession velocities are very easy to measure; all we need is an object with an emission line and a spectrograph. Distances are very difficult. This is because in order to measure a distance, we need a standard candle (an object whose luminosity is known) or a standard ruler (an object whose length is known), and we then use apparent brightness or angular size to work out the distance. Good standard candles and standard rulers are in short supply because most such objects require that we understand their astrophysics well enough to work out what their luminosity or size actually is. Neither stars nor galaxies by themselves remotely approach the uniformity needed; even when selected by other, easily measurable properties such as colour, they range over orders of magnitude in luminosity and size for reasons that are astrophysically interesting but frustrating for distance measurement. The ideal H_{0} object, in fact, is one which involves as little astrophysics as possible.
Hubble originally used a class of stars known as Cepheid variables for his distance determinations. These are giant blue stars, the best known of which is αUMa, or Polaris. In most normal stars, a selfregulating mechanism exists in which any tendency for the star to expand or contract is quickly damped out. In a small range of temperature on the HertzsprungRussell (HR) diagram, around 7000–8000 K, particularly at high luminosity,^{2} this does not happen and pulsations occur. These pulsations, the defining property of Cepheids, have a characteristic form, a steep rise followed by a gradual fall. They also have a period which is directly proportional to luminosity, because brighter stars are larger, and therefore take longer to pulsate. The periodluminosity relationship was discovered by Leavitt [123] by studying a sample of Cepheid variables in the Large Magellanic Cloud (LMC). Because these stars were known to be all at the same distance, their correlation of apparent magnitude with period therefore implied the PL relationship.
The Hubble constant was originally measured as 500 km s^{−1} Mpc^{−1} [95] and its subsequent history was a moreorless uniform revision downwards. In the early days this was caused by bias^{3} in the original samples [12], confusion between bright stars and HII regions in the original samples [97, 185] and differences between type I and II Cepheids^{4} [7]. In the second half of the last century, the subject was dominated by a lengthy dispute between investigators favouring values around 50 km s^{−1} Mpc^{−1} and those preferring higher values of 100 km s^{−1} Mpc^{−1}. Most astronomers would now bet large amounts of money on the true value lying between these extremes, and this review is an attempt to explain why and also to try and evaluate the evidence for the bestguess current value. It is not an attempt to review the global history of H_{0} determinations, as this has been done many times, often by the original protagonists or their close collaborators. For an overall review of this process see, for example, [223] and [210]. Compilations of data and analysis of them are given by Huchra (http://cfawww.harvard.edu/∼huchra/hubble), and Gott ([77], updated by [35]).^{5} Further reviews of the subject, with various different emphases and approaches, are given by [212, 68].

Has a property which allows it to be treated as either as a standard candle or as a standard ruler

Can be used independently of other calibrations (i.e., in a onestep process)

Lies at a large enough distance (a few tens of Mpc or greater) that peculiar velocities are small compared to the recession velocity at that distance

Involves as little astrophysics as possible, so that the distance determination does not depend on internal properties of the object

Provides the Hubble constant independently of other cosmological parameters.
Many different methods are discussed in this review. We begin with onestep methods, and in particular with the use of megamasers in external galaxies — arguably the only method which satisfies all the above criteria. Two other onestep methods, gravitational lensing and SunyaevZel’dovich measurements, which have significant contaminating astrophysical effects are also discussed. The review then discusses two other programmes: first, the Cepheidbased distance ladders, where the astrophysics is probably now well understood after decades of effort, but which are not onestep processes; and second, information from the CMB, an era where astrophysics is in the linear regime and therefore simpler, but where H_{0} is not determined independently of other cosmological parameters in a single experiment, without further assumptions.
1.2 A little cosmology
For the global history of the Universe in models with a cosmological constant, however, we need to consider the Λ term as providing an effective acceleration. If the cosmological constant is positive, the Universe is almost bound to expand forever, unless the matter density is very much greater than the energy density in cosmological constant and can collapse the Universe before the acceleration takes over. (A negative cosmological constant will always cause recollapse, but is not part of any currently likely world model). Carroll [34] provides further discussion of this point.
2 OneStep Distance Methods
In this section, we examine the main methods for onestep Hubble constant determination using astrophysical objects, together with their associated problems and assess the observational situation with respect to each. Other methods have been proposed^{7} but do not yet have the observations needed to apply them.
2.1 Megamaser cosmology
To determine the Hubble constant, measurements of distance are needed. In the nearby universe, the ideal object is one which is distant enough for peculiar velocities to be small — in practice around 50 Mpc — but for which a distance can be measured in one step and without a ladder of calibration involving other measurements in more nearby systems. Megamaser systems in external galaxies offer an opportunity to do this.
A megamaser system in a galaxy involves clumps of gas which are typically located ∼ 0.1 pc from the centre of the galaxy, close to the central supermassive black hole which is thought to lie at the centre of most if not all galaxies. These clumps radiate coherently in the water line at a frequency of approximately 22 GHz. This can be observed at the required milliarcsecond resolution scale using Very Long Baseline Interferometry (VLBI) techniques. With VLBI spectroscopy, the velocity of each individual clump can be measured accurately, and by repeated observations the movements of each clump can be followed and the acceleration determined. Assuming that the clumps are in Keplerian rotation, the radius of each clump from the central black hole can therefore be calculated, and the distance to the galaxy follows from knowledge of this radius together with the angular separation of the clump from the galaxy centre. The blackhole mass is also obtained as a byproduct of the analysis. The analysis is not completely straightforward, as the disk is warped and viscous, with four parameters (eccentricity, position angle, periapsis angle and inclination) describing the global properties of the disk and four further parameters describing the properties of the warping [100]. In principle it is vulnerable to systematics involving the modelling parameters not adequately describing the disk, but such systematics can be simulated for plausible extra dynamical components [100] and are likely to be small.
The first maser system to be discovered in an external galaxy was that in the object NGC 4258. This galaxy has a shell of masers which are oriented almost edgeon [136, 79] and apparently in Keplerian rotation. Measurements of the distance to this galaxy have become steadily more accurate since the original work [84, 98, 100], although the distance of ∼ 7 Mpc to this object is not sufficient to avoid large (tens of percent) systematics due to peculiar velocities in any attempt to determine H_{0}.
More recently, a systematic programme has been carried out to determine maser distances to other, more distant galaxies; the Megamaser Cosmology Project [167]. The first fruits of this programme include the measurement of the dynamics of the maser system in the galaxy UGC 3789, which have become steadily more accurate as the campaign has progressed [167, 25, 168]. A distance of 49.6±5.1 Mpc is determined, corresponding to H_{0} = 68.9±7.1 km s^{−1} Mpc^{−1} [168]; the error is dominated by the uncertainty in the likely peculiar velocity, which itself is derived from studies of the TullyFisher relation in nearby clusters [132]. Efforts are under way to find more megamasers to include in the sample, with success to date in the cases of NGC 6264 and Mrk 1419. Braatz et al. [24] and Kuo et al. [122] report preliminary results in the cases of the latter two objects, resulting in an overall determination of H_{0} = 68.0 ± 4.8 km s^{−1} Mpc^{−1} (68 ± 9 km s^{−1} Mpc^{−1} for NGC 6264). Tightening of the error bars as more megamasers are discovered, together with careful modelling, are likely to allow this project to make the cleanest determination of the Hubble constant within the next five years.
2.2 Gravitational lenses
A general review of gravitational lensing is given by Wambsganss [233]; here we review the theory necessary for an understanding of the use of lenses in determining the Hubble constant. This determination, like the megamaser method, is a onestep process, although at a much greater distance. It is thus interesting both as a complementary determination and as an opportunity to determine the Hubble parameter as a function of redshift. It has the drawback of possessing one serious systematic error associated with contaminating astrophysics, namely the detailed mass model of the lens.
2.2.1 Basics of lensing
Light is bent by the action of a gravitational field. In the case where a galaxy lies close to the line of sight to a background quasar, the quasar’s light may travel along several different paths to the observer, resulting in more than one image.
The easiest way to visualise this is to begin with a zeromass galaxy (which bends no light rays) acting as the lens, and considering all possible light paths from the quasar to the observer which have a bend in the lens plane. From the observer’s point of view, we can connect all paths which take the same time to reach the observer with a contour in the lens plane, which in this case is circular in shape. The image will form at the centre of the diagram, surrounded by circles representing increasing light travel times. This is of course an application of Fermat’s principle; images form at stationary points in the Fermat surface, in this case at the Fermat minimum. Put less technically, the light has taken a straightline path^{8} between the source and observer.
If the lens is significantly elliptical and the lines of sight are well aligned, we can produce five images, consisting of four images around a ring alternating between maxima and saddle points, and a central, highly demagnified Fermat maximum. Both fourimage and twoimage systems (“quads” and “doubles”) are in fact seen in practice. The major use of lens systems is for determining mass distributions in the lens galaxy, since the positions and fluxes of the images carry information about the gravitational potential of the lens. Gravitational lensing has the advantage that its effects are independent of whether the matter is light or dark, so in principle the effects of both baryonic and nonbaryonic matter can be probed.
2.2.2 Principles of time delays
Time delays, with 1σ errors, from the literature. In some cases multiple delays have been measured in 4image lens systems, and in this case each delay is given separately for the two components in brackets. An additional time delay for CLASS B1422+231 [151] probably requires verification, and a published time delay for Q0142100 [120, 146] has large errors. Time delays for the CLASS and PKS objects have been obtained using radio interferometers, and the remainder using optical telescopes.
Lens system  Time delay [days]  Reference 

CLASS 0218+357  10.5 ± 0.2  [16] 
HE 04351223  \(14.4_{ 0.9}^{+ 0.8}({\rm{AD}})\)  [116] 
7.8 ± 0.8 (BC)  also others [41]  
SBS 0909+532  \(45_{ 11}^{+ 1}({\rm{2}}\sigma)\)  [229] 
RX 0911+0551  146 ± 4  [86] 
FBQ 0951+2635  16 ± 2  [103] 
Q 0957+561  417 ± 3  [121] 
SDSS 1001+5027  119.3 ± 3.3  [164] 
SDSS 1004+4112  38.4 ± 2.0 (AB)  [65] 
SDSS 1029+2623  [64]  
HE 1104185  161 ± 7  [140] 
PG 1115+080  23.7 ± 3.4 (BC)  [188] 
9.4 ± 3.4 (AC)  
RX 11311231  \(12.0_{ 1.3}^{+ 1.5}({\rm{AB}})\)  [138] 
\(9.6_{ 1.6}^{+ 2.0}({\rm{AC}})\)  
87 ± 8 (AD)  
[217]  
SDSS J1206+4332  111.3 ± 3  [57] 
SBS 1520+530  130 ± 3  [30] 
CLASS 1600+434  51 ± 2  [28] 
\(47_{ 6}^{+ 5}\)  [118]  
CLASS 1608+656  \(31.5_{ 1}^{+ 2}({\rm{AB}})\)  [61] 
\(36_{ 2}^{+ 1}({\rm{BC}})\)  
\(77_{ 1}^{+ 2}({\rm{BD}})\)  
SDSS 1650+4251  49.5 ± 1.9  [230] 
PKS 1830211  \(26_{ 5}^{+ 4}\)  [127] 
WFI J20334723  35.5 ± 1.4 (AB)  [231] 
HE 21492745  103 ± 12  [29] 
HS 2209+1914  20.0 ± 5  [57] 
Q 2237+0305  \(2.7_{ 0.9}^{+ 0.5}({\rm{h}})\)  [44] 
2.2.3 The problem with lens time delays
Unlike local distance determinations (and even unlike cosmological probes which typically use more than one measurement), there is only one major systematic piece of astrophysics in the determination of H_{0} by lenses, but it is a very important one.^{11} This is the form of the potential in Eq. (11). If one parametrises the potential in the form of a power law in projected mass density versus radius, the index is −1 for an isothermal model. This index has a pretty direct degeneracy^{12} with the deduced length scale and therefore the Hubble constant; for a change of 0.1, the length scale changes by about 10%. The sense of the effect is that a steeper index, which corresponds to a more centrally concentrated mass distribution, decreases all the length scales and therefore implies a higher Hubble constant for a given time delay.
If an uncertainty in the slope of a powerlaw mass distribution were the only issue, then this could be constrained by lensing observables in the case where the source is extended, resulting in measurements of lensed structure at many different points in the lens plane [115]. This has been done, for example, using multiple radio sources [38], VLBI radio structure [239] and in many objects using lensed structure of background galaxies [21], although in this latter case H_{0} is not measurable because the background objects are not variable. The degeneracy between the Hubble constant and the mass model is more general than this, however [76]. The reason is that lensing observables give information about the derivatives of the Fermat surface; the positions of the images are determined by the first derivatives of the surface, and the fluxes by the second derivatives. For any given set of lensing observables, we can move the intrinsic source position, thus changing the Fermat surface, and then restore the observables to their original values by adjusting the mass model and thus returning the Fermat surface to its original configuration. It therefore follows that any given set of measurements of image positions and fluxes in a lens system is consistent with a number of different mass models, and therefore a number of different values of H_{0}, because the source position cannot be determined. Therefore the assumption of a particular type of model, such as a powerlaw, itself constitutes a selection of a particular one out of a range of possible models [192], each of which would give a different H_{0}. Modelling degeneracies arise not only from the mass distribution within the lens galaxy, but also from matter along the line of sight. These operate in the sense that, if a mass sheet is present which is not known about, the length scale obtained is too short and consequently the derived value of H_{0} is too high.
There are a number of approaches to this massdegeneracy problem. The first is to use a nonparametric model for the projected mass distribution, imposing only a minimum number of physicallymotivated requirements such as monotonicity, and thereby generate large numbers of mass models which are exactly consistent with the data. This was pioneered by Saha and Williams in a series of papers [179, 237, 180, 177] in which pixellated models of galaxy mass distributions were used. Although pixellated models are useful for exploring the space of allowed models, they do not break the essential degeneracy. Other priors may be used, however: in principle it should also be possible to reject some possible mass distributions on physical grounds, because we expect the mass profiles to contain a central stellar cusp and a more extended dark matter halo. Undisturbed dark matter haloes should have profiles similar to a Navarro, Frenk & White (NFW, [139]) form, but they may be modified by adiabatic contraction during the process of baryonic infall when the galaxy forms.
Second, it is possible to increase the reliability of individual lens mass models by gathering extra information which partially breaks the mass degeneracy. A major improvement is available by the use of stellar velocity dispersions [221, 220, 222, 119] measured in the lensing galaxy. As a standalone determinant of mass models in galaxies at z ∼ 0.5, typical of lens galaxies, such measurements are not very useful as they suffer from severe degeneracies with the structure of stellar orbits. However, the combination of lensing information (which gives a very accurate measurement of mass enclosed by the Einstein radius) and stellar dynamics (which gives, more or less, the mass enclosed within the effective radius of the stellar light) gives a measurement that in effect selects only some of the family of possible lens models which fit a given set of lensing observables. The method has large error bars, in part due to residual dependencies on the shape of stellar orbits, but also because these measurements are very difficult; each galaxy requires about one night of good seeing on a 10m telescope. Nevertheless, this programme has the potential beneficial effect of reducing the dominant systematic error, despite the potential additional systematic from the assumptions about stellar orbits.
Third, we can remove problems associated with mass sheets associated with material extrinsic to the main lensing galaxy by measuring them using detailed studies of the environments of lens galaxies. Studies of lens groups [60, 106, 59, 137] show that neglecting matter along the line of sight typically has an effect of 10–20%, with matter close to the redshift of the lens contributing most. More recently, it has been shown that a combination of studies of number counts and redshifts of nearby objects to the main lens galaxy, coupled with comparisons to large numerical simulations of matter such as the Millenium Simulation, can reduce the errors associated with the environment to around 3–4% [78].
2.2.4 Time delay measurements
Table 1 shows the currently measured time delays, with references and comments. The addition of new measurements is now occurring at a much faster rate, due to the advent of more systematic dedicated monitoring programmes, in particular that of the COSMOGRAIL collaboration (e.g., [230, 231, 41, 164, 57]). Considerable patience is needed for these efforts in order to determine an unambiguous delay for any given object, given the contaminating effects of microlensing and also the unavoidable gaps in the monitoring schedule (at least for optical monitoring programmes) once per year as the objects move into the daytime. Derivation of time delays under these circumstances is not a trivial matter, and algorithms which can cope with these effects have been under continuous development for decades [156, 114, 88, 217] culminating in a blind analysis challenge [50].
2.2.5 Derivation of H_{0}: Now, and the future
Initially, time delays were usually turned into Hubble constant values using assumptions about the mass model — usually that of a single, isothermal power law [119] — and with rudimentary modelling of the environment of the lens system as necessary. Early analyses of this type resulted in rather low values of the Hubble constant [112] for some systems, sometimes due to the steepness of the lens potential [221]. As the number of measured time delays expanded, combined analyses of multiple lens systems were conducted, often assuming parametric lens models [141] but also using Monte Carlo methods to account for quantities such as the presence of clusters around the main lens. These methods typically give values around 70 km s^{−1} Mpc^{−1} — e.g., (68 ± 6 ± 8) km s^{−1} Mpc^{−1} from Oguri (2007) [141], but with an uncomfortably greater spread between lens systems than would be expected on the basis of the formal errors. An alternative approach to composite modelling is to use nonparametric lens models, on the grounds that these may permit a wider range of mass distributions [177, 150] even though they also contain some level of prior assumptions. Saha et al. (2006) [177] used ten timedelay lenses for this purpose, and Paraficz et al. (2010) [150] extended the analysis to eighteen systems obtaining \(66_{ 4}^{+ 6}\), with a further extension by Sereno & Paraficz (2014) [194] giving 66 ± 6 ± 4 (stat/syst) km s^{−1} Mpc^{−1}.
In the last few years, concerted attempts have emerged to put together improved timedelay observations with systematic modelling. For two existing timedelay lenses (CLASS B1608+656 and RXJ 11311231) modelling has been undertaken [205, 206] using a combination of all of the previously described ingredients: stellar velocity dispersions to constrain the lens model and partly break the mass degeneracy, multiband HST imaging to evaluate and model the extended light distribution of the lensed object, comparison with numerical simulations to gauge the likely contribution of the line of sight to the lensing potential, and the performance of the analysis blind (without sight of the consequences for H_{0} of any decision taken during the modelling). The results of the two lenses together, \(75.2_{ 4.2}^{+ 4.4}\) and \(73.1_{ 3.6}^{+ 2.4}\) in flat and open ΛCDM, respectively, are probably the most reliable determinations of H_{0} from lensing to date, even if they do not have the lowest formal error^{13}.
In the immediate future, the most likely advances come from further analysis of existing time delay lenses, although the process of obtaining the data for good quality time delays and constraints on the mass model is not a quick process. A number of further developments will expedite the process. The first is the likely discovery of lenses on an industrial scale using the Large Synoptic Survey Telescope (LSST, [101]) and the Euclid satellite [4], together with time delays produced by high cadence monitoring. The second is the availability in a few years’ time of > 8m class optical telescopes, which will ease the followup problem considerably. A third possibility which has been discussed in the past is the use of double sourceplane lenses, in which two background objects, one of which is a quasar, are imaged by a single foreground object [74, 39]. Unfortunately, it appears [191] that even this additional set of constraints leave the mass degeneracy intact, although it remains to be seen whether dynamical information will help relatively more in these objects than in singleplane systems.
One potentially clean way to break mass model degeneracies is to discover a lensed type Ia supernova [142, 143]. The reason is that, as we have seen, the intrinsic brightness of SNe Ia can be determined from their lightcurve, and it can be shown that the resulting absolute magnification of the images can then be used to bypass the effective degeneracy between the Hubble constant and the radial mass slope. Oguri et al. [143] and also Bolton and Burles [20] discuss prospects for finding such objects; future surveys with the Large Synoptic Survey Telescope (LSST) are likely to uncover significant numbers of such events. The problem is likely to be the determination of the time delay, since nearly all such objects are subject to significant microlensing effects within the lensing galaxy which is likely to restrict the accuracy of the measurement [51].
2.3 The SunyaevZel’dovich effect
Although in principle a clean, singlestep method, in practice there are a number of possible difficulties. Firstly, the method involves two measurements, each with a list of possible errors. The Xray determination carries a calibration uncertainty and an uncertainty due to absorption by neutral hydrogen along the line of sight. The radio observation, as well as the calibration, is subject to possible errors due to subtraction of radio sources within the cluster which are unrelated to the SZ effect. Next, and probably most importantly, are the errors associated with the cluster modelling. In order to extract parameters such as electron temperature, we need to model the physics of the Xray cluster. This is not as difficult as it sounds, because Xray spectral information is usually available, and line ratio measurements give diagnostics of physical parameters. For this modelling the cluster is usually assumed to be in hydrostatic equilibrium, or a “betamodel” (a dependence of electron density with radius of the form \(n(r) = {n_0}{(1 + {r^2}/r_{\rm{c}}^2)^{ 3\beta/2}}\) is assumed. Several recent works [190, 22] relax this assumption, instead constraining the profile of the cluster with available Xray information, and the dependence of H_{0} on these details is often reassuringly small (< 10%). Finally, the cluster selection can be done carefully to avoid looking at prolate clusters along the long axis (for which l_{⊥} ≠ l_{∥}) and therefore seeing more Xrays than one would predict. This can be done by avoiding clusters close to the flux limit of Xray fluxlimited samples, Reese et al. [165] estimate an overall random error budget of 20–30% for individual clusters. As in the case of gravitational lenses, the problem then becomes the relatively trivial one of making more measurements, provided there are no unforeseen systematics.
Some recent measurements of H_{0} using the SZ effect. Model types are β for the assumption of a βmodel and H for a hydrostatic equilibrium model. Some of the studies target the same clusters, with three objects being common to more than one of the four smaller studies, The larger study [22] contains four of the objects from [104] and two from [190].
Reference  Number of clusters  Model type  H_{0} determination [km s^{−1} Mpc^{−1}] 

[22]  38  β + H  \(76.9_{ 3.4  8.0}^{+ 3.9 + 10.0}\) 
[104]  5  β  \(66_{ 10  8}^{+ 11 + 9}\) 
[228]  7  β  \(67_{ 18  6}^{+ 30 + 15}\) 
[190]  3  H  69 ± 8 
[131]  7  β  \(66_{ 11  15}^{+ 14 + 15}\) 
[165]  18  β  \(60_{ 4  18}^{+ 4 + 13}\) 
It therefore seems as though SZ determinations of the Hubble constant are beginning to converge to a value of around 70 km s^{−1} Mpc^{−1}, although the errors are still large, values in the low to midsixties are still consistent with the data and it is possible that some objects may have been observed but not used to derive a published H_{0} value. Even more than in the case of gravitational lenses, measurements of H_{0} from individual clusters are occasionally discrepant by factors of nearly two in either direction, and it would probably teach us interesting astrophysics to investigate these cases further.
2.4 Gammaray propagation
Highenergy γrays emitted by distant AGN are subject to interactions with ambient photons during their passage towards us, producing electronpositron pairs. The mean free path for this process varies with photon energy, being smaller at higher energies, and is generally a substantial fraction of the distance to the sources. The observed spectrum of γray sources therefore shows a highenergy cutoff, whose characteristic energy decreases with increasing redshift. The expected cutoff, and its dependence on redshift, has been detected with the Fermi satellite [1].
The details of this effect depend on the Hubble constant, and can therefore be used to measure it [183, 11]. Because it is an optical depth effect, knowledge of the interaction crosssection from basic physics, together with the number density n_{p} of the interacting photons, allows a length measurement and, assuming knowledge of the redshift of the source, H_{0}. In practice, the cosmological world model is also needed to determine n_{p} from observables. From the existing Fermi data a value of 72 km s^{−1} Mpc^{−1} is estimated [52] although the errors, dominated by the calculation of the evolution of the extragalactic background light using galaxy luminosity functions and spectral energy distributions, are currently quite large (∼ 10 km s^{−1} Mpc^{−1}).
3 Local Distance Ladder
3.1 Preliminary remarks
As we have seen, in principle a single object whose spectrum reveals its recession velocity, and whose distance or luminosity is accurately known, gives a measurement of the Hubble constant. In practice, the object must be far enough away for the dominant contribution to the motion to be the velocity associated with the general expansion of the Universe (the “Hubble flow”), as this expansion velocity increases linearly with distance whereas other nuisance velocities, arising from gravitational interaction with nearby matter, do not. For nearby galaxies, motions associated with the potential of the local environment are about 200–300 km s^{−1}, requiring us to measure distances corresponding to recession velocities of a few thousand km s^{−1} or greater. These recession velocities correspond to distances of at least a few tens of Mpc.
The Cepheid distance method, used since the original papers by Hubble, has therefore been to measure distances of nearby objects and use this knowledge to calibrate the brightness of more distant objects compared to the nearby ones. This process must be repeated several times in order to bootstrap one’s way out to tens of Mpc, and has been the subject of many reviews and books (see e.g., [176]). The process has a long and tortuous history, with many controversies and false turnings, and which as a byproduct included the discovery of a large amount of stellar astrophysics. The astrophysical content of the method is a disadvantage, because errors in our understanding propagate directly into errors in the distance scale and consequently the Hubble constant. The number of steps involved is also a disadvantage, as it allows opportunities for both random and systematic errors to creep into the measurement. It is probably fair to say that some of these errors are still not universally agreed on. The range of recent estimates is in the low seventies of km s^{−1} Mpc^{−1}, with the errors having shrunk by a factor of two in the last ten years, and the reasons for the disagreements (in many cases by different analysis of essentially the same data) are often quite complex.
3.2 Basic principle
We first outline the method briefly, before discussing each stage in more detail. Nearby stars have a reliable distance measurement in the form of the parallax effect. This effect arises because the earth’s motion around the sun produces an apparent shift in the position of nearby stars compared to background stars at much greater distances. The shift has a period of a year, and an angular amplitude on the sky of the EarthSun distance divided by the distance to the star. The definition of the parsec is the distance which gives a parallax of one arcsecond, and is equivalent to 3.26 lightyears, or 3.09 × 10^{16} m. The field of parallax measurement was revolutionised by the Hipparcos satellite, which measured thousands of stellar parallax distances, including observations of 223 Galactic Cepheids; of the Cepheids, 26 yielded determinations of reasonable significance [63]. The Gaia satellite will increase these by a large factor, probably observing thousands of Galactic Cepheids and giving accurate distances as well as colours and metallicities [225].
Some relatively nearby stars exist in clusters of a few hundred stars known as “open clusters”. These stars can be plotted on a HertzsprungRussell diagram of temperature, deduced from their colour together with Wien’s law, against apparent luminosity. Such plots reveal a characteristic sequence, known as the “main sequence” which ranges from red, faint stars to blue, bright stars. This sequence corresponds to the main phase of stellar evolution which stars occupy for most of their lives when they are stably burning hydrogen. In some nearby clusters, notably the Hyades, we have stars all at the same distance and for which parallax effects can give the absolute distance to <1% [159]. In such cases, the main sequence can be calibrated so that we can predict the absolute luminosity of a mainsequence star of a given colour. Applying this to other clusters, a process known as “main sequence fitting”, can also give the absolute distance to these other clusters; the errors involved in this fitting process appear to be of the order of a few percent [5].
The next stage of the bootstrap process is to determine the distance to the nearest objects outside our own Galaxy, the Large and Small Magellanic Clouds. For this we can apply the opencluster method directly, by observing open clusters in the LMC. Alternatively, we can use calibrators whose true luminosity we know, or can predict from their other properties. Such calibrators must be present in the LMC and also in open clusters (or must be close enough for their parallaxes to be directly measurable).
These calibrators include Mira variables, RR Lyrae stars and Cepheid variable stars, of which Cepheids are intrinsically the most luminous. All of these have variability periods which are correlated with their absolute luminosity (Section 1.1), and in principle the measurement of the distance of a nearby object of any of these types can then be used to determine distances to more distant similar objects simply by observing and comparing the variability periods.
The LMC lies at about 50 kpc, about three orders of magnitude less than that of the distant galaxies of interest for the Hubble constant. However, one class of variable stars, Cepheid variables, can be seen in both the LMC and in galaxies at distances up to 20–30 Mpc. The coming of the Hubble Space Telescope has been vital for this process, as only with the HST can Cepheids be reliably identified and measured in such galaxies.
Even the HST galaxies containing Cepheids are not sufficient to allow the measurement of the universal expansion, because they are not distant enough for the dominant velocity to be the Hubble flow. The final stage is to use galaxies with distances measured with Cepheid variables to calibrate other indicators which can be measured to cosmologically interesting distances. The most promising indicator consists of type Ia supernovae (SNe), which are produced by binary systems in which a giant star is dumping mass on to a white dwarf which has already gone through its evolutionary process and collapsed to an electrondegenerate remnant; at a critical point, the rate and amount of mass dumping is sufficient to trigger a supernova explosion. The physics of the explosion, and hence the observed lightcurve of the rise and slow fall, has the same characteristic regardless of distance. Although the absolute luminosity of the explosion is not constant, type Ia supernovae have similar lightcurves [163, 8, 209] and in particular there is a very good correlation between the peak brightness and the degree of fading of the supernova 15 days^{14} after peak brightness (a quantity known as Δm_{15} [162, 82]). If SNe Ia can be detected in galaxies with known Cepheid distances, this correlation can be calibrated and used to determine distances to any other galaxy in which a SN Ia is detected. Because of the brightness of supernovae, they can be observed at large distances and hence, finally, a comparison between redshift and distance will give a value of the Hubble constant.
A somewhat different indicator relies on the fact that the degree to which stars within galaxies are resolved depends on distance, in the sense that closer galaxies have more statistical “bumpiness” in the surfacebrightness distribution [219] because of the degree to which Poisson fluctuations in the stellar surface density are visible. This method of surface brightness fluctuation can also be calibrated by Cepheid variables in the nearer galaxies.
3.3 Problems and comments
3.3.1 Distance to the LMC
The LMC distance is probably the bestknown, and least controversial, part of the distance ladder. Some methods of determination are summarised in [62]; independent calibrations using RR Lyrae variables, Cepheids and open clusters, are consistent with a distance of ∼ 50 kpc. An early measurement, independent of all of the above, was made by [149] using the type II supernova SN 1987A in the LMC. This supernova produced an expanding ring whose angular diameter could be measured using the HST. An absolute size for the ring could also be deduced by monitoring ultraviolet emission lines in the ring and using light travel time arguments, and the distance of 51.2 ± 3.1 kpc followed from comparison of the two. An extension to this lightecho method was proposed in [200] which exploits the fact that the maximum in polarization in scattered light is obtained when the scattering angle is 90°. Hence, if a supernova light echo were observed in polarized light, its distance would be unambiguously calculated by comparing the lightecho time and the angular radius of the polarized ring.
More traditional calibration methods traditionally resulted in distance moduli to the LMC of μ° ≃ 18.50 (defined as 5 log d − 5, where d is the distance in parsecs) corresponding to a distance of ≃ 50 kpc. In particular, developments in the use of standardcandle stars, main sequence fitting and the details of SN 1987A are reviewed by [3] who concludes that μ^{0} = 18.50 ± 0.02. This has recently been revised downwards slightly using a more direct calibration using parallax measurements of Galactic Cepheids [14] to calibrate the zeropoint of the Cepheid PL relation in the LMC [68]. A value of μ^{0} = 18.40 ± 0.01 is found by these authors, corresponding to a distance of 47.9 ± 0.2 kpc. The likely corresponding error in H_{0} is well below the level of systematic errors in other parts of the distance ladder. This LMC distance also agrees well with the value needed in order to make the Cepheid distance to NGC 4258 agree with the maser distance ([129], see also Section 4).
3.3.2 Cepheid systematics
The details of the calibration of the Cepheid periodluminosity relation have historically caused the most difficulties in the local calibration of the Hubble constant. There are a number of minor effects, which can be estimated and calibrated relatively easy, and a dependence on metallicity which is a systematic problem upon which a lot of effort has been spent and which is now considerably better understood.
One example of a minor difficulty is a selection bias in Cepheid programmes; faint Cepheids are harder to see. Combined with the correlation between luminosity and period, this means that only the brighter shortperiod Cepheids are seen, and therefore that the PL relation in distant galaxies is made artificially shallow [186] resulting in underestimates of distances. Neglect of this bias can give differences of several percent in the answer, and detailed simulations of it have been carried out by Teerikorpi and collaborators (e.g., [214, 152, 153, 154]). Most authors correct explicitly for this problem — for example, [71] calculate the correction analytically and find a maximum bias of about 3%. Teerikorpi & Paturel suggest that a residual bias may still be present, essentially because the amplitude of variation introduces an additional scatter in brightness at a given period, in addition to the scatter in intrinsic luminosity. How big this bias is is hard to quantify, although it can in principle be eliminated by using only longperiod Cepheids at the cost of increases in the random error.
The major systematic difficulty became apparent in studies of the biggest sample of Cepheid variables, which arises from the OGLE microlensing survey of the LMC [227]. Samples of Galactic Cepheids have been studied by many authors [62, 75, 67, 10, 13, 108], and their distances can be calibrated by the methods previously described, or by using lunaroccultation measurements of stellar angular diameters [66] together with stellar temperatures to determine distances by Stefan’s law [236, 9]. Comparison of the PL relations for Galactic and LMC Cepheids, however, show significant dissimilarities. In all three HST colours (B, V, I) the slope of the relations are different, in the sense that Galactic Cepheids are brighter than LMC Cepheids at long periods and are fainter at short periods. The two samples are of equal brightness in B at a period of approximately 30 days, and at a period of a little more than 10 days in I.^{16}
The culprit for this discrepancy is mainly metallicity^{17} differences in the Cepheids, which in turn results from the fact that the LMC is more metalpoor than the Galaxy. Unfortunately, many of the external galaxies which are to be used for distance determination are likely to be similar in metallicity to the Galaxy, but the best local information on Cepheids for calibration purposes comes from the LMC. On average, the Galactic Cepheids tabulated by [81] are of approximately of solar metallicity, whereas those of the LMC are approximately 0.6 dex less metallic. If these two samples are compared with their independently derived distances, a correlation of brightness with metallicity appears with a slope of −0.8 ± 0.3 mag dex^{−1} using only Galactic Cepheids, and −0.27 ± 0.08 mag dex^{−1} using both samples together. This can cause differences of 10–15% in inferred distance if the effect is ignored.
Many areas of historic disagreement can be traced back to how this correction is done. In particular, two different 2005–2006 estimates of 73±4 (statistical) ±5 (systematic) km s^{−1} Mpc^{−1} [170] and 62.3 ± 1.3 (statistical) ±5 (systematic) km s^{−1} Mpc^{−1} [187], both based on the same Cepheid photometry from the HST Key Project [178] and essentially the same Cepheid PL relation for the LMC [218] have their origin mainly in this effect.^{18} One can apply a global correction for metallicity differences between the LMC and the galaxies in which the Cepheids are measured by the HST Key Project [181], or attempt to interpolate between LMC and Galactic PL relations [211] using a perioddependent metallicity correction [187]. The differences in this correction account for the 10–15% difference in the resulting value of H_{0}.
More recently, a number of different solutions for this problem have been found, which are summarised in the review by [68] and many of which involve getting rid of the intermediate LMC step using other calibrations. [129] use ACS observations of Cepheids in the galaxy NGC 4258, which has a welldetermined distance using maser observations (Section 4, [99, 80, 100]), and whose Cepheids have a range of metallicities [242]. Analysis of these Cepheids suggests that the use of a PL relation whose slope varies with metallicity [211, 187] overcorrects at long period. Because of the known maser distance, these Cepheids can then be used both to determine the LMC distance independently [129] and also to calibrate the SNe distance scale and hence determine H_{0} [173, 172]. The estimate has been incrementally improved by several methods in the last few years
Values obtained for the Hubble constant using the NGC 4258 calibration are quoted by [174] as 74.8 ± 3.1 km s^{−1} Mpc^{−1}, using a value of 7.28 Mpc as the NGC 4258 distance. This was later corrected by [100], who find a distance of 7.60 ± 0.17 (stat) ±0.15 (sys) Mpc using more VLBI epochs, together with better modelling of the masers, which therefore yields a Hubble constant of 72.0 ± 3.0 km s^{−1} Mpc^{−1}. Efstathiou [54] has argued for further modifications, with different criteria for rejecting outlying Cepheids; this lowers H_{0} to 70.6 ± 3.3 km s^{−1} Mpc^{−1}. The alternative distance ladder measurement, using parallax measurements of Galactic Cepheids [14] gives 75.7 ± 2.6 km s^{−1} Mpc^{−1}, and using the best available sample of LMC Cepheids observed in the infrared [160] yields 74.4 ± 2.5 km s^{−1} Mpc^{−1}. Infrared observations are important because they reduce the potential error involved in extinction corrections. Indeed, the Carnegie Hubble Programme [69] takes this further by using midIR observations (at 3.6 µm) of the Benedict et al. Galactic Cepheids with measured parallaxes, thus anchoring the calibration of the midIR PL relation in these objects, and obtaining H_{0} = 74.3 ± 2.1 km s^{−1} Mpc^{−1}. In the midIR, as well as smaller extinction corrections, metallicity effects are also generally less. However, arguments for lower values based on different outlier rejection can give a combined estimate for the three different calibrations [54] of 72.5 ± 2.5 km s^{−1} Mpc^{−1}.
3.3.3 SNe Ia systematics
The calibration of the type Ia supernova distance scale, and hence H_{0}, is affected by the selection of galaxies used which contain both Cepheids and historical supernovae. Riess et al. [170] make the case for the exclusion of a number of older supernovae from previous samples with measurements on photographic plates. Their exclusion, leaving four calibrators with data judged to be of high quality, has the effect of shrinking the average distances, and hence raising H_{0}, by a few percent. Freedman et al. [71] included six galaxies including SN 1937C, excluded by [170], but obtained approximately the same value for H_{0}.
Since SNe Ia occur in galaxies, their brightnesses are likely to be altered by extinction in the host galaxy. This effect can be assessed and, if necessary, corrected for, using information about SNe Ia colours in local SNe. The effect is found to be smaller than other systematics within the distance ladder [172].
Further possible effects include differences in SNe Ia luminosities as a function of environment. Wang et al. [234] used a sample of 109 supernovae to determine a possible effect of metallicity on SNe Ia luminosity, in the sense that supernovae closer to the centre of the galaxy (and hence of higher metallicity) are brighter. They include colour information using the indicator ΔC_{12} ≡ (B − V)_{12days}, the B − V colour at 12 days after maximum, as a means of reducing scatter in the relation between peak luminosity and Δm_{15} which forms the traditional standard candle. Their value of H_{0} is, however, quite close to the Key Project value, as they use the four galaxies of [170] to tie the supernova and Cepheid scales together. This closeness indicates that the SNe Ia environment dependence is probably a small effect compared with the systematics associated with Cepheid metallicity.
3.3.4 Other methods of establishing the distance scale
In some cases, independent distances to galaxies are available in the form of studies of the tip of the red giant branch. This phenomenon refers to the fact that metalpoor, population II red giant stars have a welldefined cutoff in luminosity which, in the Iband, does not vary much with nuisance parameters such as stellar population age. Deep imaging can therefore provide an independent standard candle which can be compared with that of the Cepheids, and in particular with the metallicity of the Cepheids in different galaxies. The result [181] is again that metalrich Cepheids are brighter, with a quoted slope of −0.24 ± 0.05 mag dex^{−1}. This agrees with earlier determinations [111, 107] and is usually adopted when a global correction is applied.
Several different methods have been proposed to bypass some of the early rungs of the distance scale and provide direct measurements of distance to relatively nearby galaxies. Many of these are reviewed in the article by Olling [144].
One of the most promising methods is the use of detached eclipsing binary stars to determine distances directly [147]. In nearby binary stars, where the components can be resolved, the determination of the angular separation, period and radial velocity amplitude immediately yields a distance estimate. In more distant eclipsing binaries in other galaxies, the angular separation cannot be measured directly. However, the lightcurve shapes provide information about the orbital period, the ratio of the radius of each star to the orbital separation, and the ratio of the stars’ luminosities. Radial velocity curves can then be used to derive the stellar radii directly. If we can obtain a physical handle on the stellar surface brightness (e.g., by study of the spectral lines) then this, together with knowledge of the stellar radius and of the observed flux received from each star, gives a determination of distance. The DIRECT project [23] has used this method to derive a distance of 964 ± 54 kpc to M33, which is higher than standard distances of 800–850 kpc [70, 124]. It will be interesting to see whether this discrepancy continues after further investigation.
A somewhat related method, but involving rotations of stars around the centre of a distant galaxy, is the method of rotational parallax [161, 145, 144]. Here one observes both the proper motion corresponding to circular rotation, and the radial velocity, of stars within the galaxy. Accurate measurement of the proper motion is difficult and will require observations from future space missions.
4 The CMB and Cosmological Estimates of the Distance Scale
4.1 The physics of the anisotropy spectrum and its implications
The physics of stellar distance calibrators is very complicated, because it comes from the era in which the Universe has had time to evolve complicated astrophysics. A large class of alternative approaches to cosmological parameters in general involve going back to an era where astrophysics is relatively simple and linear, the epoch of recombination at which the CMB fluctuations can be studied. Although tests involving the CMB do not directly determine H_{0}, they provide joint information about H_{0} and other cosmological parameters which is improving at a very rapid rate.
In the Universe’s early history, its temperature was high enough to prohibit the formation of atoms, and the Universe was therefore ionized. Approximately 4 × 10^{5} yr after the Big Bang, corresponding to a redshift z_{rec} ∼ 1000, the temperature dropped enough to allow the formation of atoms, a point known as “recombination”. For photons, the consequence of recombination was that photons no longer scattered from ionized particles but were free to stream. After recombination, these primordial photons reddened with the expansion of the Universe, forming the cosmic microwave background (CMB) which we observe today as a blackbody radiation background at 2.73 K.
In the early Universe, structure existed in the form of small density fluctuations (δρ/ρ ∼ 0.01) in the photonbaryon fluid. The resulting pressure gradients, together with gravitational restoring forces, drove oscillations, very similar to the acoustic oscillations commonly known as sound waves. Fluctuations prior to recombination could propagate at the relativistic \((c/\sqrt 3)\) sound speed as the Universe expanded. At recombination, the structure was dominated by those oscillation frequencies which had completed a halfintegral number of oscillations within the characteristic size of the Universe at recombination;^{19} this pattern became frozen into the photon field which formed the CMB once the photons and baryons decoupled and the sound speed dropped. The process is reviewed in much more detail in [92].
But the global geometry of the Universe is not the only property which can be deduced from the fluctuation spectrum.^{20} The peaks are also sensitive to the density of baryons, of total (baryonic + dark) matter, and of vacuum energy (energy associated with the cosmological constant). These densities scale with the square of the Hubble parameter times the corresponding dimensionless densities [see Eq. (5)] and measurement of the acoustic peaks therefore provides information on the Hubble constant, degenerate with other parameters, principally Ω_{m} and Ω_{Λ}. The second peak strongly constrains the baryon density, \({\Omega _{\rm{b}}}H_0^2\), and the third peak is sensitive to the total matter density in the form \({\Omega _{\rm{m}}}H_0^2\).
4.2 Degeneracies and implications for H_{0}
If we do not assume the universe to be exactly flat, as is done in Figure 9, then we obtain a degeneracy with H_{0} in the sense that decreasing H_{0} increases the total density of the universe (approximately by 0.1 in units of the critical density for a 20 km s^{−1} Mpc^{−1} decrease in H_{0}). CMB data by themselves, without any further assumptions or extra data, do not supply a significant constraint on H_{0} compared to those which are obtainable by other methods. Other observing programmes are, however, available which result in constraints on the Hubble constant together with other parameters, notably Ω_{m}, Ω_{Λ} and w (the dark energy equation of state parameter defined in Section 1.2); we can either regard w as a constant or allow a variation with redshift. We sketch these briefly here; a full review of all programmes addressing cosmic acceleration can be found in the review by Weinberg et al. [235].
The first such supplementary programme is the study of type Ia supernovae, which as we have seen function as standard candles (or at least easily calibratable candles). They therefore determine the luminosity distance D_{L}. Studies of SNe Ia were the first indication that D_{L} varies with z in such a way that an acceleration term, corresponding to a nonzero Ω_{Λ} is required [157, 158, 169], a discovery that won the 2011 Nobel Prize in physics. This determination of luminosity distance gives constraints in the Ω_{m}: Ω_{Λ} plane, which are more or less orthogonal to the CMB constraints. Currently, the most complete samples of distant SNe come from SDSS surveys at low redshift (z < 0.4) [73, 182, 89, 109], the ESSENCE survey at moderate redshift (0.1 < z < 0.78) [135, 238], the SNLS surveys at z < 1 [40] and highredshift (z > 0.6) HST surveys [171, 46, 208]. In the future, surveys in the infrared should be capable of extending the redshift range further [175].
The second important programme is the measurement of structure at more recent epochs than the epoch of recombination using the characteristic length scale frozen into the structure of matter at recombination (Section 4.1). This is manifested in the real Universe by an expected preferred correlation length of ∼ 100 Mpc between observed baryon structures, otherwise known as galaxies. These baryon acoustic oscillations (BAOs) measure a standard rod, and constrain the distance measure \({D_V} \equiv {(cz{(1 + z)^2}D_A^2H{(z)^{ 1}})^{1/3}}\) (e.g. [56]). The largest sample available for such studies comes from luminous red galaxies (LRGs) in the Sloan Digital Sky Survey [240]. The expected signal was first found [56] in the form of an increased power in the crosscorrelation between galaxies at separations of about 100 Mpc, and corresponds to an effective measurement of angular diameter distance to a redshift z ∼ 0.35. Since then, this characteristic distance has been found in other samples at different redshifts, 6dFGS at z ≃ 0.1 [15], further SDSS work at z = 0.37 [148] and by the BOSS and WiggleZ collaborations at z ≃ 0.6 [19, 6]. It has also been observed in studies of the Lyα forest [31, 199, 48]. In principle, provided the data are good enough, the BAO can be studied separately in the radial and transverse directions, giving separate constraints on D_{A} and H(z) [184, 26] and hence more straightforward and accurate cosmology.
There are a number of other programmes that constrain combinations of cosmological parameters, which can break degeneracies involving H_{0}. Weaklensing observations have progressed very substantially over the last decade, after a large programme of quantifying and reducing systematic errors; these observations consist of measuring shapes of large numbers of galaxies in order to extract the small shearing signal produced by matter along the line of sight. The quantity directly probed by such observations is a combination of Ω_{m} and σ_{8}, the rms density fluctuation at a scale of 8h^{−1} Mpc. Stateoftheart surveys include the CFHT survey [85, 110] and SDSSbased surveys [125]. Structure can also be mapped using Lymanα forest observations. The spectra of distant quasars have deep absorption lines corresponding to absorbing matter along the line of sight. The distribution of these lines measures clustering of matter on small scales and thus carries cosmological information (e.g. [226, 133]). Clustering on small scales [215] can be mapped, and the matter power spectrum can be measured, using large samples of galaxies, giving constraints on combinations of H_{0}, Ω_{m} and σ_{8}.
4.2.1 Combined constraints
As already mentioned, Planck observations of the CMB alone are capable of supplying a good constraint on H_{0}, given three assumptions: the curvature of the Universe,Ω_{k} is zero, that dark energy is a cosmological constant (w = −1) and that it is independent of redshift (w ≠ w(z)). In general, every other accurate measurement of a combination of cosmological parameters allows one to relax one of the assumptions. For example, if we admit the BAO data together with the CMB, we can allow Ω_{k} to be a free parameter [216, 6, 2]. Using earlier WMAP data for the CMB, H_{0} is derived to be 69.3 ± 1.6 km s^{−1} Mpc^{−1} [134, 6], which does not change significantly using Planck data (68.4 ± 1.0 km s^{−1} Mpc^{−1} [2]); the curvature in each case is tightly constrained (to < 0.01) and consistent with zero. If we introduce supernova data instead of BAO data, we can obtain w provided that Ω_{k} = 0 [235, 2] and this is found to be consistent with w = −1 within errors of about 0.1–0.2 [2].
If we wish to proceed further, we need to introduce additional data to get tight constraints on H_{0}. The obvious option is to use both BAO and SNe data together with the CMB, which results in H_{0} = 68.7 ± 1.9 km s^{−1} Mpc^{−1} [19] and 69.6 ± 1.7 (see Table 4 of [6]) using the WMAP CMB constraints. Such analyses continue to give low errors on H_{0} even allowing for a varying w in a nonflat universe, although they do use the results from three separate probes to achieve this. Alternatively, extrapolation of the BAO results to z = 0 give H_{0} directly [55, 15, 235] because the BAO measures a standard ruler, and the lower the redshift, the purer the standard ruler’s dependence on the Hubble constant becomes, independent of other elements in the definition of Hubble parameter such as Ω_{k} and w. The lowestredshift BAO measurement is that of the 6dF, which suggests H_{0} = 67.0 ± 3.2 km s^{−1} Mpc^{−1} [15].
5 Conclusion
Progress over the last few years in determining the Hubble constant to increasing accuracy has been encouraging and rapid. For the first time, in the form of megamaser studies, there is a onestep method available which does not have serious systematics. Simultaneously, gravitational lens time delays, also a onestep method but with a historical problem with systematics due to the mass model, has also made progress due to a combination of better simulations of the environment of the lens galaxies and better use of information which helps to ease the mass degeneracy. The classical Cepheid method has also yielded greatly improved control of systematics, mainly by moving to calibrations based on NGC 4258 and Galactic Cepheids which are much less sensitive to metallicity effects.

Megamasers: 68.0 ± 4.8 km s^{−1} Mpc^{−1} [24]. Further progress will be made by identification and monitoring of additional targets, since the systematics are likely to be well controlled using this method.

Gravitational lenses: \(73.1_{ 3.6}^{+ 2.4}\,{\rm{km}}\,{{\rm{s}}^{ 1}}\,{\rm{Mp}}{{\rm{c}}^{ 1}}\) [206] (best determination with systematics controlled, two lenses), 69±6/4 km s^{−1} Mpc^{−1} [194] (18 lenses, but errors from range of freeform modelling). Progress is likely by careful control of systematics to do with the lens mass model and the surroundings in further objects; a programme (H0LiCOW [204]) is beginning with precisely this objective.

Cepheid studies: 72.0±3.0 km s^{−1} Mpc^{−1} [174] with corrected NGC 4258 distance from [100]; 75.7± 2.6 km s^{−1} Mpc^{−1} (parallax of Galactic Cepheids) and 74.3± 2.1 km s^{−1} Mpc^{−1} (midIR observations) [69]. The Carnegie Cepheid programme is continuing IR observations which should significantly reduce systematics of the method.

For a flatbyfiat Universe, H_{0} = 67.3 ± 1.2 km s^{−1} Mpc^{−1} [2] from Planck.

For a Universe free to curve, H_{0} = 68.4 ± 1.0 km s^{−1} Mpc^{−1} [2] using Planck together with BAO data.

Local BAO measurements: H_{0} = 67.0±3.2 km s^{−1} Mpc^{−1} [15] using only the welldetermined Ω_{m}h^{2} from the CMB, but independent of other cosmology [15, 19, 6, 148].
There is thus a mild tension between some (but not all) of the astrophysical measurements and the cosmological inferences. There are several ways of looking at this. The first is that a 2.5σ discrepancy is nothing to be afraid of, and indeed is a relief after some of the clumped distributions of published measurements in the past. The second is that one or more methods are now systematicslimited; in other words, the subject is limited by accuracy rather than precision, and that careful attention to underestimated systematics will cause the values to converge in the next few years. Third, it is possible that new physics is involved beyond the variation of the dark energy index w. This new physics could, for example, involve the number of relativistic degrees of freedom being greater than the standard value of 3.05, corresponding to three active neutrino contributions [2]; or a scenario in which we are living in a local bubble with a different H_{0} [130]. Most instincts would dictate taking these possibilities in this order, unless all of the highquality astrophysical H_{0} values differed from the cosmological ones.
The argument can be turned around, by observing that independent determinations of H_{0} can be fed in as constraints to unlock a series of accurate measurements of other cosmological parameters such as w. This point has been made a number of times, in particular by Hu [91], Linder [126] and Suyu et al. [207]; the dark energy figure of merit, which measures the P − ρ dependence of dark energy and its redshift evolution, can be be improved by large factors using such independent measurements. Such measurements are usually extremely cheap in observing time (and financially) compared to other dark energy programmes. They will, however, require 1% determinations of H_{0}, given the current state of play in cosmology. This is not impossible, and should be reachable with care quite soon.
Footnotes
 1.
See [105] and references therein, e.g., [27], for discussion of the details of the interpretation of redshift in an expanding Universe. The first level of sophistication involves maintaining the GR principle that space is locally Minkowskian, so that in a small region of space all effects must reduce to SR (for instance, in Peacock’s [155] example, the expansion of the Universe does not imply that a longlived human will grow to four metres tall in the next 10^{10} years). Redshift can be thought of as a series of transformations in photon wavelengths between an infinite succession of closelyseparated observers, resulting in an overall wavelength shift between two observers with a finite separation and therefore an associated “velocity”. The second level of sophistication is to ask what this velocity actually represents. [105] calculates the ratio of photon wavelength shifts between pairs of fundamental observers to the shifts in their proper separation in the presence of arbitrary gravitational fields, and shows that this ratio only corresponds to the purely dynamical result if the gravitational tide is constant.
 2.
This is known in the literature as the “instability strip” and is almost, but not quite, parallel to the luminosity axis on the HR diagram. In normal stars, any compression of the star, and the associated rise in temperature, results in a decrease in opacity; the resulting escape of photons produces expansion and cooling. For stars in the instability strip, a layer of partially ionized He close to the surface causes opacity to rise instead of falling with an increase in temperature, producing a degree of positive feedback and consequently oscillations. The instability strip has a finite width, which causes a small degree of dispersion in periodluminosity correlations among Cepheids.
 3.
There are numerous subtle and lesssubtle biases in distance measurement; see [213] for a blowbyblow account. The simplest bias, the “classical” Malmquist bias, arises because, in any population of objects with a distribution in intrinsic luminosity, only the brighter members of the population will be seen at large distances. The result is that the inferred average luminosity is greater than the true luminosity, biasing distance measurements towards the systematically short. The Behr bias [12] from 1951 is a distancedependent version of the Malmquist bias, namely that at higher distances, increasingly bright galaxies will be missing from samples. This leads to an overestimate of the average brightness of the standard candle which becomes worse at higher distance.
 4.
Cepheids come in two flavours: type I and type II, corresponding to population I and II stars. Population II stars are an earlier metalpoor generation of stars, which formed after the hypothetical, truly primordial Population III stars, but before latergeneration Population I stars like the Sun which contain significant extra amounts of elements other than hydrogen and helium due to enrichment of the ISM by supernovae in the meantime. The name “Cepheid” derives from the fact that the star δ Cephei was the first to be identified (by Goodricke in 1784). Population II Cepheids are sometimes known as W Virginis stars, after their prototype, W Vir, and a W Vir star is typically a factor of 3 fainter than a classical Cepheid of the same period.
 5.
The conclusion of the latter, that based on median statistics of the Huchra compilation, H_{0} = 67 ± 2 km s^{−1} Mpc^{−1}, is slightly scary in retrospect given the Planck value of 67.2 ± 1.3 km s^{−1} Mpc^{−1} for a flat Universe [2].
 6.
Historically, the Hubble constant has often been quoted as H_{0} = 100h km s^{−}1 Mpc^{−1}, as a way of maintaining agnosticism in an era where observations allowed a wide range in h. This is largely disappearing, but papers using h can be hard to interpret [42]
 7.
For example, one topic that may merit more than a footnote in the future is the study of cosmology using gravitational waves. In particular, a coalescing binary system consisting of two neutron stars produces gravitational waves, and under those circumstances the measurement of the amplitude and frequency of the waves determines the distance to the object independently of the stellar masses [193]. This was studied in more detail by [36] and extended to more massive blackhole systems [90, 45]. More massive coalescing signals produce lowerfrequency gravitationalwave signals, which can be detected with the proposed LISA spacebased interferometer (http://lisa.nasa.gov/documentation.html). The major difficulty is obtaining the redshift measurement to go with the distance estimate, since the galaxy in which the coalescence event has taken place must be identified. Given this, however, the precision of the H_{0} measurement is limited only by weak gravitational lensing along the line of sight, and even this is reducible by observations of multiple systems or detailed investigations of matter along the line of sight. H_{0} determinations to ∼ 2% should be possible, but depend on the launch of LISA or a similar mission. This is an event that is probably decades away, although a pathfinder mission to test some of the technology is due for launch in 2015.
 8.
Strictly speaking, provided we ignore effects to do with curvature of the Universe.
 9.
An isothermal model is one in which the projected surface mass density decreases as 1/r. An isothermal galaxy will have a flat rotation curve, as is observed in many galaxies.
 10.
Essentially all radio time delays have come from the VLA, although monitoring programmes with MERLIN have also been attempted.
 11.
The redshifts of the lens and source also need to be known, as does the position of the centre of the lens galaxy; this measurement is not always a trivial proposition [241].
 12.
As discussed extensively in [113, 117], this is not a global degeneracy, but arises because the lensed images tell you about the mass distribution in the annulus centred on the galaxy and with inner and outer radii defined by the inner and outer images. Kochanek [113] derives detailed expressions for the time delay in terms of the central underlying and controlling parameter, the surface density in this annulus [76].
 13.
The programme, known as H0LiCOW, is now continuing in order to measure time delays, improve models and derive further H_{0} values for more lenses.
 14.
Because of the expansion of the Universe, there is a time dilation of a factor (1 + z)^{−1} which must be applied to timescales measured at cosmological distances before these are used for such comparisons.
 15.
The effective radius is the radius from within which half the galaxy’s light is emitted.
 16.
Nearly all Cepheids measured in galaxies containing SN Ia have periods > 20 days, so the usual sense of the effect is that Galactic Cepheids of a given period are brighter than LMC Cepheids.
 17.
Here, as elsewhere in astronomy, the term “metals” is used to refer to any element heavier than helium. Metallicity is usually quoted as 12+log(O/H), where O and H are the abundances of oxygen and hydrogen.
 18.
The details are discussed in more detail in an earlier version of this review [102].
 19.
This characteristic size is about 4 × 10^{5} light years at recombination, corresponding to an angular scale of about 1° on the sky. The fact that the CMB is homogeneous on scales much larger than this is an illustration of the “horizon problem” discussed in Section 1.2, and which inflation may solve.
 20.
See http://background.uchicago.edu/∼whu/intermediate/intermediate.html for a much longer exposition and tutorial on all these areas.
 21.
Notes
Acknowledgements
I thank Adam Bolton and a second anonymous referee for comments on this version of the paper, and Ian Browne, Nick Rattenbury and Sir Francis GrahamSmith for discussions and comments on the original version.
References
 [1]Ackermann, M. et al. (Fermi Collaboration), “The Imprint of the Extragalactic Background Light in the GammaRay Spectra of Blazars”, Science, 338, 1190, (2012). [DOI], [ADS], [arXiv:1211.1671]. (Cited on page 21.)ADSGoogle Scholar
 [2]Ade, P. A. R. et al. (Planck Collaboration), “Planck 2013 results. XVI. Cosmological parameters”, Astron. Astrophys., 571, A16, (2013). [DOI], [ADS], [arXiv:1303.5076]. (Cited on pages 7, 30, 31, 32, 33, and 34.)Google Scholar
 [3]Alves, D. R., “A review of the distance and structure of the Large Magellanic Cloud”, New Astron. Rev., 48, 659–665, (2004). [DOI], [ADS], [astroph/0310673]. (Cited on page 25.)ADSGoogle Scholar
 [4]Amendola, L. et al., “Cosmology and Fundamental Physics with the Euclid Satellite”, Living Rev. Relativity, 16, lrr20136 (2013). [DOI], [ADS], [arXiv:1206.1225 [astroph.CO]]. URL (accessed 7 August 2014): http://www.livingreviews.org/lrr20136. (Cited on page 19.)
 [5]An, D., Terndrup, D. M., Pinsonneault, M. H., Paulson, D. B., Hanson, R. B. and Stauffer, J. R., “The Distances to Open Clusters from MainSequence Fitting. III. Improved Accuracy with Empirically Calibrated Isochrones”, Astrophys. J., 655, 233–260, (2007). [DOI], [ADS], [astroph/0607549]. (Cited on page 23.)ADSGoogle Scholar
 [6]Anderson, L. et al., “The clustering of galaxies in the SDSSIII Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Data Release 9 spectroscopic galaxy sample”, Mon. Not. R. Astron. Soc., 427, 3435–3467, (2012). [DOI], [ADS], [arXiv:1203.6594]. (Cited on pages 32, 33, and 34.)ADSGoogle Scholar
 [7]Baade, W., “The PeriodLuminosity Relation of the Cepheids”, Publ. Astron. Soc. Pac., 68, 5–16, (1956). [DOI], [ADS]. (Cited on page 7.)ADSGoogle Scholar
 [8]Barbon, R., Ciatti, F. and Rosino, L., “Light curves and characteristics of recent supernovae”, Astron. Astrophys., 29, 57–67, (1973). [ADS]. (Cited on page 23.)ADSGoogle Scholar
 [9]Barnes, T. G. and Evans, D. S., “Stellar angular diameters and visual surface brightness. I. Late spectral types”, Mon. Not. R. Astron. Soc., 174, 489–502, (1976). [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [10]Barnes, T. G., Jefferys, W. H., Berger, J. O., Mueller, P. J., Orr, K. and Rodriguez, R., “A Bayesian Analysis of the Cepheid Distance Scale”, Astrophys. J., 592, 539–554, (2003). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [11]Barrau, A., Gorecki, A. and Grain, J., “An original constraint on the Hubble constant: h > 0.74”, Mon. Not. R. Astron. Soc., 389, 919–924, (2008). [DOI], [ADS], [arXiv:0804.3699]. (Cited on page 21.)ADSGoogle Scholar
 [12]Behr, A., “Zur Entfernungsskala der extragalaktischen Nebel”, Astron. Nachr., 279, 97, (1951). [DOI], [ADS]. (Cited on page 7.)ADSGoogle Scholar
 [13]Benedict, G. F. et al., “Astrometry with the Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator delta Cephei”, Astron. J., 124, 1695–1705, (2002). [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [14]Benedict, G. F. et al., “Hubble Space Telescope Fine Guidance Sensor Parallaxes of Galactic Cepheid Variable Stars: PeriodLuminosity Relations”, Astron. J., 133, 1810–1827, (2007). [DOI], [ADS], [arXiv:astroph/0612465]. (Cited on pages 25 and 27.)ADSGoogle Scholar
 [15]Beutler, F. et al., “The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the local Hubble Constant”, Mon. Not. R. Astron. Soc., 416, 3017–3032, (2011). [DOI], [ADS], [arXiv:1106.3366]. (Cited on pages 32, 33, and 34.)ADSGoogle Scholar
 [16]Biggs, A. D., Browne, I. W. A., Helbig, P., Koopmans, L. V. E., Wilkinson, P. N. and Perley, R. A., “Time delay for the gravitational lens system B0218+357”, Mon. Not. R. Astron. Soc., 304, 349–358, (1999). [DOI], [ADS], [astroph/9811282]. (Cited on pages 15 and 18.)ADSGoogle Scholar
 [17]Biggs, A. D., Browne, I. W. A., Muxlow, T. W. B. and Wilkinson, P. N., “MERLIN/VLA imaging of the gravitational lens system B0218+357”, Mon. Not. R. Astron. Soc., 322, 821–826, (2001). [DOI], [ADS], [astroph/0011142]. (Cited on page 15.)ADSGoogle Scholar
 [18]Birkinshaw, M., “The SunyaevZel’dovich effect”, Phys. Rep., 310, 97–195, (1999). [DOI], [ADS]. (Cited on page 19.)ADSzbMATHGoogle Scholar
 [19]Blake, C. et al., “The WiggleZ Dark Energy Survey: mapping the distanceredshift relation with baryon acoustic oscillations”, Mon. Not. R. Astron. Soc., 418, 1707–1724, (2011). [DOI], [ADS], [arXiv:1108.2635]. (Cited on pages 32, 33, and 34.)ADSGoogle Scholar
 [20]Bolton, A. S. and Burles, S., “Prospects for the Determination of H_{0} through Observation of Multiply Imaged Supernovae in Galaxy Cluster Fields”, Astrophys. J., 592, 17–23, (2003). [DOI], [ADS]. (Cited on page 19.)ADSGoogle Scholar
 [21]Bolton, A. S., Burles, S., Koopmans, L. V. E., Treu, T. and Moustakas, L. A., “The Sloan Lens ACS Survey. I. A Large Spectroscopically Selected Sample of Massive EarlyType Lens Galaxies”, Astrophys. J., 638, 703–724, (2006). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [22]Bonamente, M., Joy, M. K., LaRoque, S. J., Carlstrom, J. E., Reese, E. D. and Dawson, K. S., “Determination of the Cosmic Distance Scale from SunyaevZel’dovich Effect and Chandra XRay Measurements of HighRedshift Galaxy Clusters”, Astrophys. J., 647, 25–54, (2006). [DOI], [ADS]. (Cited on pages 20 and 21.)ADSGoogle Scholar
 [23]Bonanos, A. Z. et al., “The First DIRECT Distance Determination to a Detached Eclipsing Binary in M33”, Astrophys. J., 652, 313–322, (2006). [DOI]. (Cited on page 28.)ADSGoogle Scholar
 [24]Braatz, J. et al., “Measuring the Hubble constant with observations of watervapor megamasers”, in de Grijs, R., ed., Advancing the Physics of Cosmic Distances, Proceedings of IAU Symposium 289, August 2012, Proc. IAU, 289, pp. 255–261, (Cambridge University Press, Cambridge, 2013). [DOI], [ADS]. (Cited on pages 12 and 34.)Google Scholar
 [25]Braatz, J. A., Reid, M. J., Humphreys, E. M. L., Henkel, C., Condon, J. J. and Lo, K. Y., “The Megamaser Cosmology Project. II. The Angulardiameter Distance to UGC 3789”, Astrophys. J., 718, 657–665, (2010). [DOI], [ADS], [arXiv:1005.1955]. (Cited on page 12.)ADSGoogle Scholar
 [26]Bull, P., Ferreira, P. G., Patel, P. and Santos, M. G., “Latetime cosmology with 21 cm intensity mapping experiments”, Astrophys. J., 803, 21, (2014). [DOI], [ADS], [arXiv:1405.1452]. (Cited on page 32.)ADSGoogle Scholar
 [27]Bunn, E. F. and Hogg, D. W., “The kinematic origin of the cosmological redshift”, Am. J. Phys., 77, 688–694, (2009). [DOI], [ADS], [arXiv:0808.1081 [physics.popph]]. (Cited on page 5.)ADSGoogle Scholar
 [28]Burud, I. et al., “An Optical Time Delay Estimate for the Double Gravitational Lens System B1600+434”, Astrophys. J., 544, 117–122, (2000). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [29]Burud, I. et al., “An optical timedelay for the lensed BAL quasar HE 21492745”, Astron. Astrophys., 383, 71–81, (2002). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [30]Burud, I. et al., “Time delay and lens redshift for the doubly imaged BAL quasar SBS 1520+530”, Astron. Astrophys., 391, 481, (2002). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [31]Busca, N. G. et al., “Baryon acoustic oscillations in the Lyα forest of BOSS quasars”, Astron. Astrophys., 552, A96, (2013). [DOI], [ADS], [arXiv:1211.2616 [astroph.CO]]. (Cited on page 32.)Google Scholar
 [32]Caldwell, R. R., Kamionkowski, M. and Weinberg, N. N., “Phantom Energy: Dark Energy with w < 1 Causes a Cosmic Doomsday”, Phys. Rev. Lett., 91, 071301, (2003). [DOI], [ADS], [astroph/0302506]. (Cited on page 9.)ADSGoogle Scholar
 [33]Carlstrom, J. E., Holder, G. P. and Reese, E. D., “Cosmology with the SunyaevZel’dovich Effect”, Annu. Rev. Astron. Astrophys., 40, 643–680, (2002). [DOI], [ADS]. (Cited on page 19.)ADSGoogle Scholar
 [34]Carroll, S. M., “The Cosmological Constant”, Living Rev. Relativity, 4, lrr20011 (2001). [DOI], [ADS]. URL (accessed 8 May 2007): http://www.livingreviews.org/lrr20011. (Cited on pages 8 and 9.)
 [35]Chen, G., Gott III, J. R. and Ratra, B., “NonGaussian Error Distribution of Hubble Constant Measurements”, Publ. Astron. Soc. Pac., 115, 1269–1279, (2003). [DOI], [ADS], [astroph/0308099]. (Cited on page 7.)ADSGoogle Scholar
 [36]Chernoff, D. F. and Finn, L. S., “Gravitational radiation, inspiraling binaries, and cosmology”, Astrophys. J., 411, L5–L8, (1993). [DOI], [arXiv:grqc/9304020]. (Cited on page 11.)ADSGoogle Scholar
 [37]Cheung, C. C. et al., “Fermi Large Area Telescope Detection of Gravitational Lens Delayed γRay Flares from Blazar B0218+357”, Astrophys. J. Lett., 782, L14, (2014). [DOI], [ADS], [arXiv:1401.0548]. (Cited on pages 14 and 15.)ADSGoogle Scholar
 [38]Cohn, J. D., Kochanek, C. S., McLeod, B. A. and Keeton, C. R., “Constraints on Galaxy Density Profiles from Strong Gravitational Lensing: The Case of B1933+503”, Astrophys. J., 554, 1216–1226, (2001). [DOI], [ADS], [arXiv:astroph/0008390]. (Cited on page 16.)ADSGoogle Scholar
 [39]Collett, T. E., Auger, M. W., Belokurov, V., Marshall, P. J. and Hall, A. C., “Constraining the dark energy equation of state with doublesource plane strong lenses”, Mon. Not. R. Astron. Soc., 424, 2864, (2012). [DOI], [ADS], [arXiv:1203.2758]. (Cited on page 19.)ADSGoogle Scholar
 [40]Conley, A. et al., “Supernova Constraints and Systematic Uncertainties from the First Three Years of the Supernova Legacy Survey”, Astrophys. J. Suppl. Ser., 192, 1, (2011). [DOI], [ADS], [arXiv:1104.1443]. (Cited on page 32.)ADSGoogle Scholar
 [41]Courbin, F. et al., “COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses. IX. Time delays, lens dynamics and baryonic fraction in HE 04351223”, Astron. Astrophys., 536, A53, (2011). [DOI], [ADS], [arXiv:1009.1473]. (Cited on pages 17 and 18.)Google Scholar
 [42]Croton, D. J., “Damn You, Little h! (Or, RealWorld Applications of the Hubble Constant Using Observed and Simulated Data)”, Publ. Astron. Soc. Australia, 30, e052 (2013). [DOI], [ADS], [arXiv:1308.4150 [astroph.CO]]. (Cited on page 9.)ADSGoogle Scholar
 [43]Curtis, H. D., “Modern Theories of the Spiral Nebulae”, J. R. Astron. Soc. Can., 14, 317–327, (1920). [ADS]. (Cited on page 5.)ADSGoogle Scholar
 [44]Dai, X., Chartas, G., Agol, E., Bautz, M. W. and Garmire, G. P., “Chandra Observations of QSO 2237+0305”, Astrophys. J., 589, 100–110, (2003). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [45]Dalal, N., Holz, D. E., Hughes, S. A. and Jain, B., “Short GRB and binary black hole standard sirens as a probe of dark energy”, Phys. Rev. D, 74, 063006, (2006). [DOI], [ADS], [astroph/0601275]. (Cited on page 11.)ADSGoogle Scholar
 [46]Dawson, K. S. et al. (Supernova Cosmology Project), “An Intensive Hubble Space Telescope Survey for z > 1 Type Ia Supernovae by Targeting Galaxy Clusters”, Astron. J., 138, 1271–1283, (2009). [DOI], [ADS], [arXiv:0908.3928]. (Cited on page 32.)ADSGoogle Scholar
 [47]de Bernardis, P. et al., “A flat Universe from highresolution maps of the cosmic microwave background radiation”, Nature, 404, 955–959, (2000). [DOI], [ADS], [arXiv:astroph/0004404]. (Cited on page 29.)ADSGoogle Scholar
 [48]Delubac, T. et al., “Baryon acoustic oscillations in the Lyα forest of BOSS DR11 quasars”, Astron. Astrophys., 574, A59, (2015). [DOI], [ADS], [arXiv:1404.1801]. (Cited on page 32.)Google Scholar
 [49]Djorgovski, S. and Davis, M., “Fundamental properties of elliptical galaxies”, Astrophys. J., 313, 59–68, (1987). [DOI], [ADS]. (Cited on page 23.)ADSGoogle Scholar
 [50]Dobler, G., Fassnacht, C., Treu, T., Marshall, P. J., Liao, K., Hojjati, A., Linder, E. and Rumbaugh, N., “Strong Lens Time Delay Challenge. I. Experimental Design”, Astrophys. J., 799, 168, (2015).[DOI], [ADS], [arXiv:1310.4830]. (Cited on page 17.)ADSGoogle Scholar
 [51]Dobler, G. and Keeton, C. R., “Microlensing of Lensed Supernovae”, Astrophys. J., 653, 1391–1399, (2006). [DOI], [ADS], [astroph/0608391]. (Cited on page 19.)ADSGoogle Scholar
 [52]Domínguez, A. and Prada, F., “Measurement of the Expansion Rate of the Universe from γray Attenuation”, Astrophys. J., 771, L34, (2013). [DOI], [ADS], [arXiv:1305.2163]. (Cited on page 21.)ADSGoogle Scholar
 [53]Dressler, A., LyndenBell, D., Burstein, D., Davies, R. L., Faber, S. M., Terlevich, R. and Wegner, G., “Spectroscopy and photometry of elliptical galaxies. I — A new distance estimator”, Astrophys. J., 313, 42–58, (1987). [DOI], [ADS]. (Cited on page 23.)ADSGoogle Scholar
 [54]Efstathiou, G., “H_{0} revisited”, Mon. Not. R. Astron. Soc., 440, 1138–1152, (2014). [DOI], [ADS], [arXiv:1311.3461 [astroph.CO]]. (Cited on pages 26 and 27.)ADSGoogle Scholar
 [55]Eisenstein, D. J., Hu, W. and Tegmark, M., “Cosmic Complementarity: H_{0} and Ω_{m} from combining Cosmic Microwave Background experiments and redshift surveys”, Astrophys. J., 504, L57–L60, (1998). [DOI], [ADS], [astroph/9805239]. (Cited on page 33.)ADSGoogle Scholar
 [56]Eisenstein, D. J. et al., “Detection of the Baryon Acoustic Peak in the LargeScale Correlation Function of SDSS Luminous Red Galaxies”, Astrophys. J., 633, 560–574, (2005). [DOI], [ADS], [arXiv:astroph/0501171]. (Cited on page 32.)ADSGoogle Scholar
 [57]Eulaers, E. et al., “COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses. XII. Time delays of the doubly lensed quasars SDSS J1206+4332 and HS 2209+1914”, Astron. Astrophys., 553, A121, (2013). [DOI], [ADS], [arXiv:1304.4474]. (Cited on pages 17 and 18.)Google Scholar
 [58]Faber, S. M. and Jackson, R. E., “Velocity dispersions and masstolight ratios for elliptical galaxies”, Astrophys. J., 204, 668–683, (1976). [DOI], [ADS]. (Cited on page 23.)ADSGoogle Scholar
 [59]Fassnacht, C. D., Gal, R. R., Lubin, L. M., McKean, J. P., Squires, G. K. and Readhead, A. C. S., “Mass along the Line of Sight to the Gravitational Lens B1608+656: Galaxy Groups and Implications for H_{0}”, Astrophys. J., 642, 30–38 (2006). [DOI], [ADS]. (Cited on page 17.)ADSGoogle Scholar
 [60]Fassnacht, C. D. and Lubin, L. M., “The Gravitational LensGalaxy Group Connection. I. Discovery of a Group Coincident with CLASS B0712+472”, Astron. J., 123, 627–636, (2002). [DOI], [ADS]. (Cited on page 17.)ADSGoogle Scholar
 [61]Fassnacht, C. D., Xanthopoulos, E., Koopmans, L. V. E. and Rusin, D., “A Determination of H_{0}with the CLASS Gravitational Lens B1608+656. III. A Significant Improvement in the Precision of the Time Delay Measurements”, Astrophys. J., 581, 823–835, (2002). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [62]Feast, M. W., “The Distance to the Large Magellanic Cloud; A Critical Review”, in Chu, Y.H., Suntzeff, N. B., Hesser, J. E. and Bohlender, D. A., eds., New Views of the Magellanic Clouds, Proceedings of the 190th Symposium of the IAU, held in Victoria, BC, Canada, July 12–17, 1998, 190, pp. 542–548, (Astronomical Society of the Pacific, San Francisco, 1999). [ADS]. (Cited on pages 25 and 26.)Google Scholar
 [63]Feast, M. W. and Catchpole, R. M., “The Cepheid periodluminosity zeropoint from HIPPARCOS trigonometrical parallaxes”, Mon. Not. R. Astron. Soc., 286, L1–L5, (1997). [DOI], [ADS]. (Cited on page 22.)ADSGoogle Scholar
 [64]Fohlmeister, J., Kochanek, C. S., Falco, E. E., Wambsganss, J., Oguri, M. and Dai, X., “A Twoyear Time Delay for the Lensed Quasar SDSS J1029+2623”, Astrophys. J., 764, 186, (2013). [DOI], [ADS], [arXiv:1207.5776]. (Cited on page 18.)ADSGoogle Scholar
 [65]Fohlmeister, J. et al., “A Time Delay for the Largest Gravitationally Lensed Quasar: SDSSJ1004+4112”, arXiv, eprint, (2006). [ADS], [arXiv:astroph/0607513]. (Cited on page 18.)Google Scholar
 [66]Fouque, P. and Gieren, W. P., “An improved calibration of Cepheid visual and infrared surface brightness relations from accurate angular diameter measurements of cool giants and supergiants”, Astron. Astrophys., 320, 799–810, (1997). [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [67]Fouque, P., Storm, J. and Gieren, W., “Calibration of the Distance Scale from Cepheids”, in Alloin, D. and Gieren, W., eds., Stellar Candles for the Extragalactic Distance Scale, Lecture Notes in Physics, 635, pp. 21–44, (Springer, Berlin; New York, 2003). [DOI]. (Cited on page 26.)Google Scholar
 [68]Freedman, W. L. and Madore, B. F., “The Hubble Constant”, Annu. Rev. Astron. Astrophys., 48, 673–710, (2010). [DOI], [ADS], [arXiv:1004.1856]. (Cited on pages 7, 25, and 26.)ADSGoogle Scholar
 [69]Freedman, W. L., Madore, B. F., Scowcroft, V., Burns, C., Monson, A., Persson, S. E., Seibert, M. and Rigby, J., “Carnegie Hubble Program: A Midinfrared Calibration of the Hubble Constant”, Astrophys. J., 758, 24, (2012). [DOI], [ADS], [arXiv:1208.3281]. (Cited on pages 27 and 34.)ADSGoogle Scholar
 [70]Freedman, W. L., Wilson, C. D. and Madore, B. F., “New Cepheid distances to nearby galaxies based on BVRI CCD photometry. II. The local group galaxy M33”, Astrophys. J., 372, 455–470, (1991). [DOI], [ADS]. (Cited on page 28.)ADSGoogle Scholar
 [71]Freedman, W. L. et al. (HST Collaboration), “Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant”, Astrophys. J., 553, 47–72, (2001). [DOI], [ADS]. (Cited on pages 25 and 27.)ADSGoogle Scholar
 [72]Friedman, A. A., “Über die Krümmung des Raumes”, Z. Phys., 10, 377–386, (1922). [DOI]. English translation in Cosmological Constants: Papers in Modern Cosmology, eds. Bernstein, J. and Feinberg, G., (Columbia University Press, New York, 1986). (Cited on page 8.)ADSGoogle Scholar
 [73]Frieman, J. A. et al. (SDSS Collaboration), “The Sloan Digital Sky SurveyII Supernova Survey: Technical Summary”, Astron. J., 135, 338–347, (2008). [DOI], [ADS], [arXiv:0708.2749]. (Cited on page 32.)ADSGoogle Scholar
 [74]Gavazzi, R., Treu, T., Koopmans, L. V. E., Bolton, A. S., Moustakas, L. A., Burles, S. and Marshall, P. J., “The Sloan Lens ACS Survey. VI. Discovery and Analysis of a Double Einstein Ring”, Astrophys. J., 677, 1046–1059, (2008). [DOI], [ADS], [arXiv:0801.1555]. (Cited on page 19.)ADSGoogle Scholar
 [75]Gieren, W. P., Fouqué, P. and Gómez, M., “Cepheid PeriodRadius and PeriodLuminosity Relations and the Distance to the Large Magellanic Cloud”, Astrophys. J., 496, 17–30, (1998). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [76]Gorenstein, M. V., Shapiro, I. I. and Falco, E. E., “Degeneracies in parameter estimation in models of gravitational lens systems”, Astrophys. J., 327, 693–711, (1988). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [77]Gott III, J. R., Vogeley, M. S., Podariu, S. and Ratra, B., “Median Statistics, H_{0} and the Accelerating Universe”, Astrophys. J., 549, 1–17, (2001). [DOI], [ADS], [astroph/0006103]. (Cited on page 7.)ADSGoogle Scholar
 [78]Greene, Z. S. et al., “Improving the Precision of Timedelay Cosmography with Observations of Galaxies along the Line of Sight”, Astrophys. J., 768, 39, (2013). [DOI], [ADS], [arXiv:1303.3588]. (Cited on page 17.)ADSGoogle Scholar
 [79]Greenhill, L. J., Jiang, D. R., Moran, J. M., Reid, M. J., Lo, K. Y. and Claussen, M. J., “Detection of a Subparsec Diameter Disk in the Nucleus of NGC 4258”, Astrophys. J., 440, 619–627, (1995). [DOI], [ADS]. (Cited on page 11.)ADSGoogle Scholar
 [80]Greenhill, L. J., Kondratko, P. T., Moran, J. M. and Tilak, A., “Discovery of Candidate H_{2}O Disk Masers in Active Galactic Nuclei and Estimations Of Centripetal Accelerations”, Astrophys. J., 707, 787–799, (2009). [DOI], [ADS], [arXiv:0911.0382]. (Cited on page 26.)ADSGoogle Scholar
 [81]Groenewegen, M. A. T., Romaniello, M., Primas, F. and Mottini, M., “The metallicity dependence of the Cepheid PLrelation”, Astron. Astrophys., 420, 655–663, (2004). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [82]Hamuy, M., Phillips, M. M., Suntzeff, N. B., Schommer, R. A., Maza, J., Smith, R. C., Lira, P. and Aviles, R., “The Morphology of Type Ia Supernovae Light Curves”, Astron. J., 112, 2438–2447, (1996). [DOI], [ADS], [astroph/9609059]. (Cited on page 23.)ADSGoogle Scholar
 [83]Hanany, S. et al., “MAXIMA1: A Measurement of the Cosmic Microwave Background Anisotropy on Angular Scales of 10′–5°”, Astrophys. J. Lett., 545, L5–L9, (2000). [DOI], [ADS], [astroph/0005123]. (Cited on page 29.)ADSGoogle Scholar
 [84]Herrnstein, J. R. et al., “A geometric distance to the galaxy NGC4258 from orbital motions in a nuclear gas disk”, Nature, 400, 539–541, (1999). [DOI], [ADS]. (Cited on page 11.)ADSGoogle Scholar
 [85]Heymans, C. et al., “CFHTLenS: the CanadaFranceHawaii Telescope Lensing Survey”, Mon. Not. R. Astron. Soc., 427, 146–166, (2012). [DOI], [ADS], [arXiv:1210.0032]. (Cited on page 32.)ADSGoogle Scholar
 [86]Hjorth, J. et al., “The Time Delay of the Quadruple Quasar RX J0911.4+0551”, Astrophys. J., 572, L11–L14, (2002). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [87]Hogg, D. W., “Distance measures in cosmology”, arXiv, eprint, (1999). [ADS], [arXiv:astroph/9905116]. (Cited on page 10.)Google Scholar
 [88]Hojjati, A., Kim, A. G. and Linder, E. V., “Robust strong lensing time delay estimation”, Phys. Rev. D, 87, 123512, (2013). [DOI], [ADS], [arXiv:1304.0309]. (Cited on page 17.)ADSGoogle Scholar
 [89]Holtzman, J. A. et al., “The Sloan Digital Sky SurveyII: Photometry and Supernova IA Light Curves from the 2005 Data”, Astron. J., 136, 2306–2320, (2008). [DOI], [ADS], [arXiv:0908.4277]. (Cited on page 32.)ADSGoogle Scholar
 [90]Holz, D. E. and Hughes, S. A., “Using GravitationalWave Standard Sirens”, Astrophys. J., 629, 15–22, (2005). [DOI], [ADS], [arXiv:astroph/0504616]. (Cited on page 11.)ADSGoogle Scholar
 [91]Hu, W., “Dark Energy Probes in Light of the CMB”, in Wolff, S. C. and Lauer, T. R., eds., Observing Dark Energy, Proceedings of a meeting held in Tucson, AZ, USA, March 18–20, 2004, ASP Conference Series, 339, pp. 215–234, (Astronomical Society of the Pacific, San Francisco, 2005). [ADS]. (Cited on page 35.)Google Scholar
 [92]Hu, W. and Dodelson, S., “Cosmic Microwave Background Anisotropies”, Annu. Rev. Astron. Astrophys., 40, 171–216, (2002). [DOI], [ADS]. (Cited on page 29.)ADSGoogle Scholar
 [93]Hubble, E. P., “NGC 6822, a remote stellar system”, Astrophys. J., 62, 409–433, (1925). [DOI], [ADS]. (Cited on page 5.)ADSGoogle Scholar
 [94]Hubble, E. P., “A spiral nebula as a stellar system: Messier 33”, Astrophys. J., 63, 236–274, (1926). [DOI], [ADS]. (Cited on page 5.)ADSGoogle Scholar
 [95]Hubble, E. P., “A Relation between Distance and Radial Velocity among ExtraGalactic Nebulae”, Proc. Natl. Acad. Sci. USA, 15, 168–173, (1929). [DOI], [ADS]. (Cited on pages 6 and 7.)ADSzbMATHGoogle Scholar
 [96]Hubble, E. P., “A spiral nebula as a stellar system, Messier 31”, Astrophys. J., 69, 103–158, (1929). [DOI], [ADS]. (Cited on page 5.)ADSGoogle Scholar
 [97]Humason, M. L., Mayall, N. U. and Sandage, A. R., “Redshifts and magnitudes of extragalactic nebulae”, Astron. J., 61, 97–162, (1956). [DOI], [ADS]. (Cited on page 7.)ADSGoogle Scholar
 [98]Humphreys, E. M. L., Argon, A. L., Greenhill, L. J., Moran, J. M. and Reid, M. J., “Recent Progress on a New Distance to NGC 4258”, in Romney, J. D. and Reid, M. J., eds., Future Directions in High Resolution Astronomy: The 10th Anniversary of the VLBA, Proceedings of a meeting held in Socorro, NM, USA, June 8–12, 2003, ASP Conference Series, 340, pp. 466–470, (Astronomical Society of the Pacific, San Francisco, 2005). [ADS]. (Cited on page 11.)Google Scholar
 [99]Humphreys, E. M. L., Reid, M. J., Greenhill, L. J., Moran, J. M. and Argon, A. L., “Toward a New Geometric Distance to the Active Galaxy NGC 4258. II. Centripetal Accelerations and Investigation of Spiral Structure”, Astrophys. J., 672, 800–816, (2008). [DOI], [ADS], [arXiv:0709.0925]. (Cited on page 26.)ADSGoogle Scholar
 [100]Humphreys, E. M. L., Reid, M. J., Moran, J. M., Greenhill, L. J. and Argon, A. L., “Toward a New Geometric Distance to the Active Galaxy NGC 4258. III. Final Results and the Hubble Constant”, Astrophys. J., 775, 13, (2013). [DOI], [ADS], [arXiv:1307.6031]. (Cited on pages 11, 26, and 34.)ADSGoogle Scholar
 [101]Ivezić, Ž. et al. (LSST Collaboration), “LSST: from Science Drivers to Reference Design and Anticipated Data Products”, arXiv, eprint, (2008). [ADS], [arXiv:0805.2366]. (Cited on page 19.)Google Scholar
 [102]Jackson, N., “The Hubble Constant”, Living Rev. Relativity, 10, lrr20074 (2007). [DOI], [ADS]. URL (accessed 6 March 2014): http://www.livingreviews.org/lrr20074. (Cited on page 26.)
 [103]Jakobsson, P., Hjorth, J., Burud, I., Letawe, G., Lidman, C. and Courbin, F., “An optical time delay for the double gravitational lens system FBQ 0951+2635”, Astron. Astrophys., 431, 103–109, (2005). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [104]Jones, M. E. et al., “H_{0} from an orientationunbiased sample of SunyaevZel’dovich and Xray clusters”, Mon. Not. R. Astron. Soc., 357, 518–526, (2005). [DOI], [ADS]. (Cited on pages 20 and 21.)ADSGoogle Scholar
 [105]Kaiser, N., “Astronomical redshifts and the expansion of space”, Mon. Not. R. Astron. Soc., 438, 2456–2465, (2014). [DOI], [ADS], [arXiv:1312.1190 [astroph.CO]]. (Cited on page 5.)ADSGoogle Scholar
 [106]Keeton, C. R. and Zabludoff, A. I., “The Importance of Lens Galaxy Environments”, Astrophys. J., 612, 660–678, (2004). [DOI], [ADS]. (Cited on page 17.)ADSGoogle Scholar
 [107]Kennicutt Jr, R. C., Bresolin, F. and Garnett, D. R., “The Composition Gradient in M101 Revisited. II. Electron Temperatures and Implications for the Nebular Abundance Scale”, Astrophys. J., 591, 801–820, (2003). [DOI], [ADS]. (Cited on page 27.)ADSGoogle Scholar
 [108]Kervella, P., Nardetto, N., Bersier, D., Mourard, D. and Coudé du Foresto, V., “Cepheid distances from infrared longbaseline interferometry. I. VINCI/VLTI observations of seven Galactic Cepheids”, Astron. Astrophys., 416, 941–953, (2004). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [109]Kessler, R. et al., “FirstYear Sloan Digital Sky SurveyII Supernova Results: Hubble Diagram and Cosmological Parameters”, Astrophys. J. Suppl. Ser., 185, 32–84, (2009). [DOI], [ADS], [arXiv:0908.4274]. (Cited on page 32.)ADSGoogle Scholar
 [110]Kilbinger, M. et al., “CFHTLenS: combined probe cosmological model comparison using 2D weak gravitational lensing”, Mon. Not. R. Astron. Soc., 430, 2200–2220, (2013). [DOI], [ADS], [arXiv:1212.3338]. (Cited on page 32.)ADSGoogle Scholar
 [111]Kochanek, C. S., “Rebuilding the Cepheid Distance Scale. I. A Global Analysis of Cepheid Mean Magnitudes”, Astrophys. J., 491, 13–28, (1997). [DOI], [ADS]. (Cited on page 27.)ADSGoogle Scholar
 [112]Kochanek, C. S., “What Do Gravitational Lens Time Delays Measure?”, Astrophys. J., 578, 25–32, (2002). [DOI], [ADS]. (Cited on page 17.)ADSGoogle Scholar
 [113]Kochanek, C. S., “Part 2: Strong Gravitational Lensing”, in Meylan, G., Jetzer, P. and North, P., eds., Gravitational Lensing: Strong, Weak and Micro, SaasFee Advanced Courses, 33, pp. 91–268, (Springer, Berlin; New York, 2004). [ADS]. (Cited on page 16.)Google Scholar
 [114]Kochanek, C. S., “Quantitative interpretation of quasar microlensing light curves”, Astrophys. J., 605, 58–77, (2004). [DOI], [ADS]. (Cited on page 17.)ADSGoogle Scholar
 [115]Kochanek, C. S., Keeton, C. R. and McLeod, B. A., “The Importance of Einstein Rings”, Astrophys. J., 547, 50–59, (2001). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [116]Kochanek, C. S., Morgan, N. D., Falco, E. E., McLeod, B. A., Winn, J. N., Dembicky, J. and Ketzeback, B., “The Time Delays of Gravitational Lens HE 0435–1223: An EarlyType Galaxy with a Rising Rotation Curve”, Astrophys. J., 640, 47–61, (2006). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [117]Kochanek, C. S. and Schechter, P. L., “The Hubble Constant from Gravitational Lens Time Delays”, in Freedman, W. L., ed., Measuring and Modeling the Universe, Carnegie Observatories Centennial Symposium 2, Pasadena, CA, 17–22 September 2002, Carnegie Observatories Astrophysics Series, 2, pp. 117–137, (Cambridge University Press, Cambridge; New York, 2004). [ADS]. (Cited on page 16.)Google Scholar
 [118]Koopmans, L. V. E., de Bruyn, A. G., Xanthopoulos, E. and Fassnacht, C. D., “A timedelay determination from VLA light curves of the CLASS gravitational lens B1600+434”, Astron. Astrophys., 356, 391–402, (2000). [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [119]Koopmans, L. V. E., Treu, T., Bolton, A. S., Burles, S. and Moustakas, L. A., “The Sloan Lens ACS Survey. III. The Structure and Formation of EarlyType Galaxies and Their Evolution since z ∼ 1”, Astrophys. J., 640, 599–615, (2006). [DOI], [ADS]. (Cited on pages 16 and 17.)ADSGoogle Scholar
 [120]Koptelova, E., Oknyanskij, V. L., Artamonov, B. P. and Burkhonov, O., “Intrinsic quasar variability and time delay determination in the lensed quasar UM673”, Mon. Not. R. Astron. Soc., 401, 2805–2815, (2010). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [121]Kundić, T. et al., “A Robust Determination of the Time Delay in 0957+561A, B and a Measurement of the Global Value of Hubble’s Constant”, Astrophys. J., 482, 75–82, (1997). [DOI], [ADS]. (Cited on pages 14 and 18.)ADSGoogle Scholar
 [122]Kuo, C. Y., Braatz, J. A., Reid, M. J., Lo, K. Y., Condon, J. J., Impellizzeri, C. M. V. and Henkel, C., “The Megamaser Cosmology Project. V. An Angulardiameter Distance to NGC 6264 at 140 Mpc”, Astrophys. J., 767, 155, (2013). [DOI], [ADS], [arXiv:1207.7273]. (Cited on page 12.)ADSGoogle Scholar
 [123]Leavitt, H. S. and Pickering, E. C., Periods of 25 Variable Stars in the Small Magellanic Cloud, Harvard College Observatory Circular, 173, (Harvard College Observatory, Cambridge, 1912). [ADS]. (Cited on page 7.)Google Scholar
 [124]Lee, M. G., Kim, M., Sarajedini, A., Geisler, D. and Gieren, W., “Determination of the Distance to M33 Based on SingleEpoch IBand Hubble Space Telescope Observations of Cepheids”, Astrophys. J., 565, 959–965, (2002). [DOI], [ADS]. (Cited on page 28.)ADSGoogle Scholar
 [125]Lin, H. et al., “The SDSS coadd: cosmic shear measurement”, Astrophys. J., 761, 15, (2012). [DOI], [ADS]. (Cited on page 32.)ADSGoogle Scholar
 [126]Linder, E. V., “Lensing time delays and cosmological complementarity”, Phys. Rev. D, 84, 123529, (2011). [DOI], [ADS], [arXiv:1109.2592 [astroph.CO]]. (Cited on page 35.)ADSGoogle Scholar
 [127]Lovell, J. E. J., Jauncey, D. L., Reynolds, J. E., Wieringa, M. H., King, E. A., Tzioumis, A. K., McCulloch, P. M. and Edwards, P. G., “The Time Delay in the Gravitational Lens PKS 1830211”, Astrophys. J. Lett., 508, L51–L54, (1998). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [128]LyndenBell, D., Burstein, D., Davies, R. L., Dressler, A. and Faber, S. M., “On best distance estimators and galaxy streaming”, in van den Bergh, S. and Pritchet, C. J., eds., The Extragalactic Distance Scale, Proceedings of the ASP 100th Anniversary Symposium, held in Victoria, BC, Canada, June 29–July 1, 1988, ASP Conference Series, 4, pp. 307–316, (Astronomical Society of the Pacific, San Francisco, 1988). [ADS]. (Cited on page 23.)Google Scholar
 [129]Macri, L. M., Stanek, K. Z., Bersier, D., Greenhill, L. J. and Reid, M. J., “A New Cepheid Distance to the MaserHost Galaxy NGC 4258 and Its Implications for the Hubble Constant”, Astrophys. J., 652, 1133–1149, (2006). [DOI], [ADS]. (Cited on pages 24, 25, and 26.)ADSGoogle Scholar
 [130]Marra, V., Amendola, L., Sawicki, I. and Valkenburg, W., “Cosmic Variance and the Measurement of the Local Hubble Parameter”, Phys. Rev. Lett., 110, 241305, (2013). [DOI], [ADS], [arXiv:1303.3121 [astroph.CO]]. (Cited on page 34.)ADSGoogle Scholar
 [131]Mason, B. S., Myers, S. T. and Readhead, A. C. S., “A Measurement of H_{0} from the SunyaevZeldovich Effect”, Astrophys. J. Lett., 555, L11–L15, (2001). [DOI], [ADS]. (Cited on page 21.)ADSGoogle Scholar
 [132]Masters, K. L., Springob, C. M., Haynes, M. P. and Giovanelli, R., “SFI++ I: A New IBand TullyFisher Template, the Cluster Peculiar Velocity Dispersion, and H_{0}”, Astrophys. J., 653, 861–880, (2006). [DOI], [ADS], [astroph/0609249]. (Cited on page 12.)ADSGoogle Scholar
 [133]McDonald, P. et al., “The linear theory power spectrum from the Lyα forest in the sloan digital sky survey”, Astrophys. J., 635, 761–783, (2005). [DOI], [ADS], [astroph/0407377]. (Cited on page 32.)ADSGoogle Scholar
 [134]Mehta, K. T., Cuesta, A. J., Xu, X., Eisenstein, D. J. and Padmanabhan, N., “A 2 per cent distance to z = 0.35 by reconstructing baryon acoustic oscillations — III. Cosmological measurements and interpretation”, Mon. Not. R. Astron. Soc., 427, 2168–2179, (2012). [DOI], [ADS], [arXiv:1202.0092 [astroph.CO]]. (Cited on page 32.)ADSGoogle Scholar
 [135]Miknaitis, G. et al., “The ESSENCE Supernova Survey: Survey Optimization, Observations, and Supernova Photometry”, Astrophys. J., 666, 674–693, (2007). [DOI], [ADS], [arXiv:astroph/0701043]. (Cited on page 32.)ADSGoogle Scholar
 [136]Miyoshi, M., Moran, J., Herrnstein, J., Greenhill, L., Nakai, N., Diamond, P. and Inoue, M., “Evidence for a Black Hole from High Rotation Velocities in a SubParsec Region of NGC4258”, Nature, 373, 127–129, (1995). [DOI], [ADS]. (Cited on page 11.)ADSGoogle Scholar
 [137]Momcheva, I., Williams, K. A., Keeton, C. R. and Zabludoff, A. I., “A Spectroscopic Study of the Environments of Gravitational Lens Galaxies”, Astrophys. J., 641, 169–189, (2006). [DOI], [ADS]. (Cited on page 17.)ADSGoogle Scholar
 [138]Morgan, N. D., Kochanek, C. S., Falco, E. E. and Dai, X., “TimeDelays and Mass Models for the Quadruple Lens RXJ11311231”, 2007 AAS/AAPT Joint Meeting held in Seattle, WA, USA, January 5–10, 2007, conference paper, (2006). [ADS]. AAS Poster 021.07. (Cited on page 18.)Google Scholar
 [139]Navarro, J. F., Frenk, C. S. and White, S. D. M., “The Structure of Cold Dark Matter Halos”, Astrophys. J., 462, 563–575, (1996). [DOI], [ADS], [arXiv:astroph/9508025]. (Cited on page 16.)ADSGoogle Scholar
 [140]Ofek, E. O. and Maoz, D., “TimeDelay Measurement of the Lensed Quasar HE 11041805”, Astrophys. J., 594, 101–106, (2003). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [141]Oguri, M., “Gravitational Lens Time Delays: A Statistical Assessment of Lens Model Dependences and Implications for the Global Hubble Constant”, Astrophys. J., 660, 1–15, (2007). [DOI], [ADS]. (Cited on page 17.)ADSGoogle Scholar
 [142]Oguri, M. and Kawano, Y., “Gravitational lens time delays for distant supernovae: breaking the degeneracy between radial mass profiles and the Hubble constant”, Mon. Not. R. Astron. Soc., 338, L25–L29, (2003). [DOI], [ADS]. (Cited on page 19.)ADSGoogle Scholar
 [143]Oguri, M., Suto, Y. and Turner, E. L., “Gravitational Lensing Magnification and Time Delay Statistics for Distant Supernovae”, Astrophys. J., 583, 584–593, (2003). [DOI], [ADS]. (Cited on page 19.)ADSGoogle Scholar
 [144]Olling, R. P., “Accurate ExtraGalactic Distances and Dark Energy: Anchoring the Distance Scale with Rotational Parallaxes”, arXiv, eprint, (2006). [arXiv:astroph/0607607]. (Cited on pages 27 and 28.)Google Scholar
 [145]Olling, R. P. and Peterson, D. M., “Galaxy Distances via Rotational Parallaxes”, arXiv, eprint, (2000). [arXiv:astroph/0005484]. (Cited on page 28.)Google Scholar
 [146]Oscoz, A., SerraRicart, M., Mediavilla, E. and Muñoz, J. A., “Longterm Monitoring, Time Delay, and Microlensing in the Gravitational Lens System Q0142100”, Astrophys. J., 779, 144, (2013). [DOI], [ADS], [arXiv:1310.6569]. (Cited on page 18.)ADSGoogle Scholar
 [147]Paczyński, B., “Detached Eclipsing Binaries as Primary Distance and Age Indicators”, in Livio, M., Donahue, M. and Panagia, N., eds., The Extragalactic Distance Scale, Proceedings of the ST ScI May Symposium, held in Baltimore, MD, May 7–10, 1996, Space Telescope Science Institute Symposium Series, pp. 273–280, (Cambridge University Press, Cambridge; New York, 1997). (Cited on page 27.)Google Scholar
 [148]Padmanabhan, N., Xu, X., Eisenstein, D. J., Scalzo, R., Cuesta, A. J., Mehta, K. T. and Kazin, E., “A 2 per cent distance to z = 0.35 by reconstructing baryon acoustic oscillations — I. Methods and application to the Sloan Digital Sky Survey”, Mon. Not. R. Astron. Soc., 427, 2132–2145, (2012). [DOI], [ADS], [arXiv:1202.0090]. (Cited on pages 32 and 34.)ADSGoogle Scholar
 [149]Panagia, N., Gilmozzi, R., Macchetto, F., Adorf, H.M. and Kirshner, R. P., “Properties of the SN 1987A circumstellar ring and the distance to the Large Magellanic Cloud”, Astrophys. J. Lett., 380, L23–L26, (1991). [DOI], [ADS]. (Cited on page 25.)ADSGoogle Scholar
 [150]Paraficz, D. and Hjorth, J., “The Hubble Constant Inferred from 18 Timedelay Lenses”, Astrophys. J., 712, 1378, (2010). [DOI], [ADS], [arXiv:1002.2570]. (Cited on page 17.)ADSGoogle Scholar
 [151]Patnaik, A. R. and Narasimha, D., “Determination of time delay from the gravitational lens B1422+231”, Mon. Not. R. Astron. Soc., 326, 1403–1411, (2001). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [152]Paturel, G. and Teerikorpi, P., “The extragalactic Cepheid distance bias: Numerical simulations”, Astron. Astrophys., 413, L31–L34, (2004). [DOI], [ADS]. (Cited on page 25.)ADSGoogle Scholar
 [153]Paturel, G. and Teerikorpi, P., “The extragalactic Cepheid bias: significant influence on the cosmic distance scale”, Astron. Astrophys., 443, 883–889, (2005). [DOI], [ADS]. (Cited on page 25.)ADSGoogle Scholar
 [154]Paturel, G. and Teerikorpi, P., “The extragalactic Cepheid bias: a new test using the periodluminositycolor relation”, Astron. Astrophys., 452, 423–430, (2006). [DOI], [ADS]. (Cited on page 25.)ADSGoogle Scholar
 [155]Peacock, J. A., Cosmological Physics, (Cambridge University Press, Cambridge; New York, 1999). [ADS], [Google Books]. (Cited on pages 5 and 10.)zbMATHGoogle Scholar
 [156]Pelt, J., Kayser, R., Refsdal, S. and Schramm, T., “The light curve and the time delay of QSO 0957+561”, Astron. Astrophys., 305, 97, (1996). [ADS], [arXiv:astroph/9501036]. (Cited on page 17.)ADSGoogle Scholar
 [157]Perlmutter, S. et al., “Measurements of the Cosmological Parameters Omega and Lambda from the First Seven Supernovae at z ≥ 0.35”, Astrophys. J., 483, 565–581, (1997). [DOI], [ADS]. (Cited on pages 8 and 32.)ADSGoogle Scholar
 [158]Perlmutter, S. et al. (Supernova Cosmology Project), “Measurements of Ω and Λ from 42 HighRedshift Supernovae”, in Paul, J., Montmerle, T. and Aubourg, E., eds., Abstracts of the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, Paris, France, December 14–18, 1998, p. 146, (Aubourg (CEA Saclay), Paris, 1998). (Cited on page 32.)Google Scholar
 [159]Perryman, M. A. C. et al., “The Hyades: distance, structure, dynamics, and age”, Astron. Astrophys., 331, 81–120, (1998). [ADS], [astroph/9707253]. (Cited on page 22.)ADSGoogle Scholar
 [160]Persson, S. E., Madore, B. F., Krzemiński, W., Freedman, W. L., Roth, M. and Murphy, D. C., “New Cepheid PeriodLuminosity Relations for the Large Magellanic Cloud: 92 NearInfrared Light Curves”, Astron. J., 128, 2239–2264, (2004). [DOI], [ADS]. (Cited on page 27.)ADSGoogle Scholar
 [161]Peterson, D. and Shao, M., “The Scientific Basis for the Space Interferometry Mission”, in Battrick, B., ed., Hipparcos Venice’ 97 Symposium: Presenting The Hipparcos and Tycho Catalogues and first astrophysical results of the Hipparcos astrometry mission, Proceedings of the ESA Symposium, Venice, Italy, May 13–16, 1997, SP402, pp. 749–753, (ESA Publications Division, Noordwijk, 1997). [ADS]. Online version (accessed 10 September 2007): http://www.rssd.esa.int/?project=HIPPARCOS&page=venice97. (Cited on page 28.)Google Scholar
 [162]Phillips, M. M., “The absolute magnitudes of Type Ia supernovae”, Astrophys. J. Lett., 413, L105–L108, (1993). [DOI], [ADS]. (Cited on page 23.)ADSGoogle Scholar
 [163]Pskovskii, Y. P., “The Photometric Properties of Supernovae”, Sov. Astron., 11, 63–69, (1967). [ADS]. (Cited on page 23.)ADSGoogle Scholar
 [164]Rathna Kumar, S. et al., “COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses. XIV. Time delay of the doubly lensed quasar SDSS J1001+5027”, Astron. Astrophys., 557, A44, (2013). [DOI], [ADS], [arXiv:1306.5105]. (Cited on pages 17 and 18.)Google Scholar
 [165]Reese, E. D., Carlstrom, J. E., Joy, M., Mohr, J. J., Grego, L. and Holzapfel, W. L., “Determining the Cosmic Distance Scale from Interferometric Measurements of the SunyaevZeldovich Effect”, Astrophys. J., 581, 53–85, (2002). [DOI], [ADS]. (Cited on pages 20 and 21.)ADSGoogle Scholar
 [166]Refsdal, S., “On the possibility of determining Hubble’s parameter and the masses of galaxies from the gravitational lens effect”, Mon. Not. R. Astron. Soc., 128, 307–310, (1964). [ADS]. (Cited on page 13.)ADSMathSciNetzbMATHGoogle Scholar
 [167]Reid, M. J., Braatz, J. A., Condon, J. J., Greenhill, L. J., Henkel, C. and Lo, K. Y., “The Megamaser Cosmology Project. I. Very Long Baseline Interferometric Observations of UGC 3789”, Astrophys. J., 695, 287–291, (2009). [DOI], [ADS], [arXiv:0811.4345]. (Cited on pages 11 and 12.)ADSGoogle Scholar
 [168]Reid, M. J., Braatz, J. A., Condon, J. J., Lo, K. Y., Kuo, C. Y., Impellizzeri, C. M. V. and Henkel, C., “The Megamaser Cosmology Project. IV. A Direct Measurement of the Hubble Constant from UGC 3789”, Astrophys. J., 767, 154, (2013). [DOI], [ADS], [arXiv:1207.7292]. (Cited on page 12.)ADSGoogle Scholar
 [169]Riess, A. G. et al., “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant”, Astron. J., 116, 1009–1038, (1998). [DOI], [ADS], [arXiv:astroph/9805201]. (Cited on pages 8 and 32.)ADSGoogle Scholar
 [170]Riess, A. G. et al., “Cepheid Calibrations from the Hubble Space Telescope of the Luminosity of Two Recent Type Ia Supernovae and a Redetermination of the Hubble Constant”, Astrophys. J., 627, 579–607, (2005). [DOI], [ADS]. (Cited on pages 26 and 27.)ADSGoogle Scholar
 [171]Riess, A. G. et al., “New Hubble Space Telescope discoveries of Type Ia supernovae at z ≥ 1: Narrowing constraints on the early behaviour of dark energy”, Astrophys. J., 659, 98–121, (2007). [DOI], [ADS], [arXiv:astroph/0611572]. (Cited on page 32.)ADSGoogle Scholar
 [172]Riess, A. G. et al., “Cepheid Calibrations of Modern Type Ia Supernovae: Implications for the Hubble Constant”, Astrophys. J. Suppl. Ser., 183, 109–141, (2009). [DOI], [ADS], [arXiv:0905.0697]. (Cited on pages 26 and 27.)ADSGoogle Scholar
 [173]Riess, A. G. et al., “A Redetermination of the Hubble Constant with the Hubble Space Telescope from a Differential Distance Ladder”, Astrophys. J., 699, 539–563, (2009). [DOI], [ADS], [arXiv:0905.0695]. (Cited on page 26.)ADSGoogle Scholar
 [174]Riess, A. G. et al., “A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3”, Astrophys. J., 730, 119, (2011). [DOI], [ADS], [arXiv:1103.2976]. (Cited on pages 26 and 34.)ADSGoogle Scholar
 [175]Rodney, S. A. et al., “A Type Ia Supernova at Redshift 1.55 in Hubble Space Telescope Infrared Observations from CANDELS”, Astrophys. J., 746, 5, (2012). [DOI], [ADS], [arXiv:1201.2470]. (Cited on page 32.)ADSGoogle Scholar
 [176]RowanRobinson, M., The Cosmological Distance Ladder: Distance and Time in the Universe, (W.H. Freeman, New York, 1985). (Cited on pages 5 and 22.)Google Scholar
 [177]Saha, P., Coles, J., Macció, A. V. and Williams, L. L. R., “The Hubble Time Inferred from 10 Time Delay Lenses”, Astrophys. J. Lett., 650, L17–L20, (2006). [DOI], [ADS]. (Cited on pages 16 and 17.)ADSGoogle Scholar
 [178]Saha, P., Coles, J., Macció, A. V. and Williams, L. L. R., “The Hubble Time Inferred from 10 Time Delay Lenses”, Astrophys. J., 650, L17–L20, (2006). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [179]Saha, P. and Williams, L. L. R., “Nonparametric reconstruction of the galaxy lens in PG 1115+080”, Mon. Not. R. Astron. Soc., 292, 148–156, (1997). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [180]Saha, P. and Williams, L. L. R., “Beware the Nonuniqueness of Einstein Rings”, Astron. J., 122, 585–590, (2001). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [181]Sakai, S., Ferrarese, L., Kennicutt Jr, R. C. and Saha, A., “The Effect of Metallicity on Cepheidbased Distances”, Astrophys. J., 608, 42–61, (2004). [DOI], [ADS]. (Cited on pages 26 and 27.)ADSGoogle Scholar
 [182]Sako, M. et al., “The Sloan Digital Sky SurveyII Supernova Survey: Search Algorithm and Followup Observations”, Astron. J., 135, 348–373, (2008). [DOI], [ADS], [arXiv:0708.2750]. (Cited on page 32.)ADSGoogle Scholar
 [183]Salamon, M. H., Stecker, F. W. and de Jager, O. C., “A new method for determining the Hubble constant from subTeV gammaray observations”, Astrophys. J., 423, L1–L4, (1994). [DOI], [ADS]. (Cited on page 21.)ADSGoogle Scholar
 [184]Sánchez, E., Alonso, D., Sánchez, F. J., GarcíaBellido, J. and Sevilla, I., “Precise measurement of the radial baryon acoustic oscillation scales in galaxy redshift surveys”, Mon. Not. R. Astron. Soc., 434, 2008–2019, (2013). [DOI], [ADS], [arXiv:1210.6446 [astroph.CO]]. (Cited on page 32.)ADSGoogle Scholar
 [185]Sandage, A., “Current Problems in the Extragalactic Distance Scale”, Astrophys. J., 127, 513–526, (1958). [DOI], [ADS]. (Cited on page 7.)ADSGoogle Scholar
 [186]Sandage, A., “Cepheids as distance indicators when used near their detection limit”, Publ. Astron. Soc. Pac., 100, 935–948, (1988). [DOI], [ADS]. (Cited on page 25.)ADSGoogle Scholar
 [187]Sandage, A., Tammann, G. A., Saha, A., Reindl, B., Macchetto, F. D. and Panagia, N., “The Hubble Constant: A Summary of the Hubble Space Telescope Program for the Luminosity Calibration of Type Ia Supernovae by Means of Cepheids”, Astrophys. J., 653, 843–860, (2006). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [188]Schechter, P. L. et al., “The Quadruple Gravitational Lens PG 1115+080: Time Delays and Models”, Astrophys. J. Lett., 475, L85–L88, (1997). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [189]Schild, R. and Thomson, D. J., “The Q0957+561 Time Delay From Optical Data”, Astron. J., 113, 130–135, (1997). [DOI], [ADS]. (Cited on page 14.)ADSGoogle Scholar
 [190]Schmidt, R. W., Allen, S. W. and Fabian, A. C., “An improved approach to measuring H_{0} using Xray and SZ observations of galaxy clusters”, Mon. Not. R. Astron. Soc., 352, 1413–1420, (2004). [DOI], [ADS]. (Cited on pages 20 and 21.)ADSGoogle Scholar
 [191]Schneider, P., “Can one determine cosmological parameters from multiplane strong lens systems?”, Astron. Astrophys., 568, L2, (2014). [DOI], [ADS], [arXiv:1406.6152]. (Cited on page 19.)ADSGoogle Scholar
 [192]Schneider, P. and Sluse, D., “Masssheet degeneracy, powerlaw models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing”, Astron. Astrophys., 559, A37, (2013). [DOI], [ADS], [arXiv:1306.0901]. (Cited on page 16.)ADSGoogle Scholar
 [193]Schutz, B. F., “Determining the Hubble Constant from Gravitational Wave Observations”, Nature, 323, 310–311, (1986). [DOI], [ADS]. (Cited on page 11.)ADSGoogle Scholar
 [194]Sereno, M. and Paraficz, D., “Hubble constant and dark energy inferred from freeform determined time delay distances”, Mon. Not. R. Astron. Soc., 437, 600–605, (2014). [DOI], [ADS], [arXiv:1310.2251]. (Cited on pages 17 and 34.)ADSGoogle Scholar
 [195]Shapley, H., “On the Existence of External Galaxies”, J. R. Astron. Soc. Can., 13, 438–446, (1919). [ADS]. (Cited on page 5.)ADSGoogle Scholar
 [196]Silk, J. and White, S. D. M., “The determination of Q_{0} using Xray and microwave observations of galaxy clusters”, Astrophys. J. Lett., 226, L103–L106, (1978). [DOI], [ADS]. (Cited on page 19.)ADSGoogle Scholar
 [197]Slipher, V. M., “The Radial Velocity of the Andromeda Nebula”, Popular Astron., 22, 19–21, (1914). [ADS]. (Cited on page 5.)ADSGoogle Scholar
 [198]Slipher, V. M., “Radial velocity observations of spiral nebulae”, Observatory, 40, 304–306, (1917). [ADS]. (Cited on page 5.)ADSGoogle Scholar
 [199]Slosar, A. et al., “Measurement of baryon acoustic oscillations in the Lymanα forest fluctuations in BOSS data release 9”, J. Cosmol. Astropart. Phys., 2013(04), 026, (2013). [DOI], [ADS], [arXiv:1301.3459 [astroph.CO]]. (Cited on page 32.)Google Scholar
 [200]Sparks, W. B., “A direct way to measure the distances of galaxies”, Astrophys. J., 433, 19–28, (1994). [DOI], [ADS]. (Cited on page 25.)ADSGoogle Scholar
 [201]Spergel, D. N. et al. (WMAP Collaboration), “FirstYear Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters”, Astrophys. J. Suppl. Ser., 148, 175–194, (2003). [DOI], [ADS]. (Cited on pages 29 and 31.)ADSGoogle Scholar
 [202]Spergel, D. N. et al., “ThreeYear Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology”, Astrophys. J. Suppl. Ser., 170, 377–408, (2007). [DOI], [ADS], [arXiv:astroph/0603449]. (Cited on pages 29 and 31.)ADSGoogle Scholar
 [203]Sunyaev, R. A. and Zel’dovich, Y. B., “The Observations of Relic Radiation as a Test of the Nature of XRay Radiation from the Clusters of Galaxies”, Comments Astrophys. Space Phys., 4, 173–178, (1972). [ADS]. (Cited on page 19.)ADSGoogle Scholar
 [204]Suyu, S., “Gravitational Lens Time Delays: Past, Present and Future”, The Return of de Sitter II, Max Planck Institute for Astrophysics, Garching, Germany, October 14–18, 2013, conference paper, (2013). URL (accessed 7 August 2014): http://wwwmpa.mpagarching.mpg.de/∼komatsu/meetings/ds2013/schedule/suyu_desitterii.pdf. (Cited on page 34.)
 [205]Suyu, S. H., Marshall, P. J., Auger, M. W., Hilbert, S., Blandford, R. D., Koopmans, L. V. E., Fassnacht, C. D. and Treu, T., “Dissecting the Gravitational lens B1608+656. II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State”, Astrophys. J., 711, 201–221, (2010). [DOI], [ADS], [arXiv:0910.2773]. (Cited on page 17.)ADSGoogle Scholar
 [206]Suyu, S. H. et al., “Two Accurate Timedelay Distances from Strong Lensing: Implications for Cosmology”, Astrophys. J., 766, 70, (2013). [DOI], [ADS], [arXiv:1208.6010]. (Cited on pages 17 and 34.)ADSGoogle Scholar
 [207]Suyu, S. H. et al., “Cosmology from gravitational lens time delays and Planck data”, Astrophys. J., 788, L35, (2014). [DOI], [ADS], [arXiv:1306.4732]. (Cited on page 35.)ADSGoogle Scholar
 [208]Suzuki, N. et al. (Supernova Cosmology Project), “The Hubble Space Telescope Cluster Supernova Survey. V. Improving the Darkenergy Constraints above z > 1 and Building an Earlytypehosted Supernova Sample”, Astrophys. J., 746, 85, (2012). [DOI], [ADS], [arXiv:1105.3470]. (Cited on page 32.)ADSGoogle Scholar
 [209]Tammann, G. A., “Supernova statistics and related problems”, in Rees, M. J. and Stoneham, R. J., eds., Supernovae: A Survey of Current Research, Proceedings of the NATO Advanced Study Institute, held at Cambridge, UK, June 29–July 10, 1981, NATO Science Series C, 90, pp. 371–403, (Kluwer, Dordrecht; Boston, 1982). [ADS]. (Cited on page 23.)Google Scholar
 [210]Tammann, G. A. and Reindl, B., “Karl Schwarzschild Lecture: The Ups and Downs of the Hubble Constant”, in Röser, S., ed., The Many Facets of the Universe — Revelations by New Instruments, Herbsttagung 2005 / 79th Annual Scientific Meeting of the Astronomische Gesellschaft, Cologne, Germany, September 26–October 1, 2005, Reviews in Modern Astronomy, 19, pp. 1–30, (WileyVCH, Weinheim, 2006). [ADS], [astroph/0512584]. (Cited on page 7.)Google Scholar
 [211]Tammann, G. A., Sandage, A. and Reindl, B., “New PeriodLuminosity and PeriodColor relations of classical Cepheids: I. Cepheids in the Galaxy”, Astron. Astrophys., 404, 423–448, (2003). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [212]Tammann, G. A., Sandage, A. and Reindl, B., “The expansion field: the value of H_{0}”, Astron. Astrophys. Rev., 15, 289–331, (2008). [DOI], [ADS]. (Cited on page 7.)ADSGoogle Scholar
 [213]Teerikorpi, P., “Observational Selection Bias Affecting the Determination of the Extragalactic Distance Scale”, Annu. Rev. Astron. Astrophys., 35, 101–136, (1997). [DOI], [ADS]. (Cited on page 7.)ADSGoogle Scholar
 [214]Teerikorpi, P. and Paturel, G., “Evidence for the extragalactic Cepheid distance bias from the kinematical distance scale”, Astron. Astrophys., 381, L37–L40, (2002). [DOI], [ADS]. (Cited on page 25.)ADSGoogle Scholar
 [215]Tegmark, M. et al. (SDSS Collaboration), “The ThreeDimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey”, Astrophys. J., 606, 702–740, (2004). [DOI], [ADS], [arXiv:astroph/0310725]. (Cited on page 32.)ADSGoogle Scholar
 [216]Tegmark, M. et al. (SDSS Collaboration), “Cosmological constraints from the SDSS luminous red galaxies”, Phys. Rev. D, 74, 123507, (2006). [DOI], [ADS]. (Cited on page 32.)ADSGoogle Scholar
 [217]Tewes, M., Courbin, F. and Meylan, G., “COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses. XI. Techniques for time delay measurement in presence of microlensing”, Astron. Astrophys., 553, A120, (2013). [DOI], [ADS], [arXiv:1208.5598]. (Cited on pages 17 and 18.)ADSGoogle Scholar
 [218]Thim, F., Tammann, G. A., Saha, A., Dolphin, A., Sandage, A., Tolstoy, E. and Labhardt, L., “The Cepheid Distance to NGC 5236 (M83) with the ESO Very Large Telescope”, Astrophys. J., 590, 256–270, (2003). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [219]Tonry, J. and Schneider, D. P., “A new technique for measuring extragalactic distances”, Astron. J., 96, 807–815, (1988). [DOI], [ADS]. (Cited on page 25.)ADSGoogle Scholar
 [220]Treu, T. and Koopmans, L. V. E., “The Internal Structure and Formation of EarlyType Galaxies: The Gravitational Lens System MG 2016+112 at z = 1.004”, Astrophys. J., 575, 87–94, (2002). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [221]Treu, T. and Koopmans, L. V. E., “The internal structure of the lens PG1115+080: breaking degeneracies in the value of the Hubble constant”, Mon. Not. R. Astron. Soc., 337, L6–L10, (2002). [DOI], [ADS], [astroph/0210002]. (Cited on pages 16 and 17.)ADSGoogle Scholar
 [222]Treu, T. and Koopmans, L. V. E., “Massive Dark Matter Halos and Evolution of EarlyType Galaxies to z ∼ 1”, Astrophys. J., 611, 739–760, (2004). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [223]Trimble, V., “H_{0}: The Incredible Shrinking Constant, 1925–1975”, Publ. Astron. Soc. Pac., 108, 1073–1082, (1996). [DOI], [ADS]. (Cited on page 7.)ADSGoogle Scholar
 [224]Tully, R. B. and Fisher, J. R., “A new method of determining distances to galaxies”, Astron. Astrophys., 54, 661–673, (1977). [ADS]. (Cited on page 23.)ADSGoogle Scholar
 [225]Turon, C., Luri, X. and Masana, E., “Building the cosmic distance scale: from Hipparcos to Gaia”, Astrophys. Space Sci., 341, 15–29, (2012). [DOI], [ADS], [arXiv:1202.3645 [astroph.IM]]. (Cited on page 22.)ADSGoogle Scholar
 [226]Tytler, D. et al., “Cosmological Parameters σ_{8}, the Baryon Density Ω_{b}, the Vacuum Energy Density Ω_{Λ}, the Hubble Constant and the UV Background Intensity from a Calibrated Measurement of H I Lyα Absorption at z = 1.9”, Astrophys. J., 617, 1–28, (2004). [DOI], [ADS]. (Cited on page 32.)ADSGoogle Scholar
 [227]Udalski, A., Soszynski, I., Szymański, M., Kubiak, M., Pietrzynski, G., Wozniak, P. and Zebrun, K., “The Optical Gravitational Lensing Experiment. Cepheids in the Magellanic Clouds. IV. Catalog of Cepheids from the Large Magellanic Cloud”, Acta Astron., 49, 223–317, (1999). [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [228]Udomprasert, P. S., Mason, B. S., Readhead, A. C. S. and Pearson, T. J., “An Unbiased Measurement of H_{0} through Cosmic Background Imager Observations of the SunyaevZel’dovich Effect in Nearby Galaxy Clusters”, Astrophys. J., 615, 63–81, (2004). [DOI], [ADS]. (Cited on page 21.)ADSGoogle Scholar
 [229]Ullán, A., Goicoechea, L. J., Zheleznyak, A. P., Koptelova, E., Bruevich, V. V., Akhunov, T. and Burkhonov, O., “Time delay of SBS 0909+532”, Astron. Astrophys., 452, 25–35, (2006). [DOI], [ADS]. (Cited on page 18.)ADSGoogle Scholar
 [230]Vuissoz, C. et al., “COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses. V. The time delay in SDSS J1650+4251”, Astron. Astrophys., 464, 845–851, (2007). [DOI], [ADS]. (Cited on pages 17 and 18.)ADSGoogle Scholar
 [231]Vuissoz, C. et al., “COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses. VII. Time delays and the Hubble constant from WFI J20334723”, Astron. Astrophys., 488, 481–490, (2008). [DOI], [ADS], [arXiv:0803.4015]. (Cited on pages 17 and 18.)ADSGoogle Scholar
 [232]Walsh, D., Carswell, R. F. and Weymann, R. J., “0957 + 561 A, B: twin quasistellar objects or gravitational lens?”, Nature, 279, 381–384, (1979). [DOI], [ADS]. (Cited on page 14.)ADSGoogle Scholar
 [233]Wambsganss, J., “Gravitational Lensing in Astronomy”, Living Rev. Relativity, 1, lrr199812 (1998). [DOI], [ADS], [astroph/9812021]. URL (accessed 25 June 2007): http://www.livingreviews.org/lrr199812. (Cited on pages 12 and 14.)
 [234]Wang, X., Wang, L., Pain, R., Zhou, X. and Li, Z., “Determination of the Hubble Constant, the Intrinsic Scatter of Luminosities of Type Ia Supernovae, and Evidence for Nonstandard Dust in Other Galaxies”, Astrophys. J., 645, 488–505, (2006). [DOI], [ADS]. (Cited on page 27.)ADSGoogle Scholar
 [235]Weinberg, D. H., Mortonson, M. J., Eisenstein, D. J., Hirata, C., Riess, A. G. and Rozo, E., “Observational probes of cosmic acceleration”, Phys. Rep., 530, 87–255, (2013). [DOI], [ADS], [arXiv:1201.2434]. (Cited on pages 8, 32, and 33.)ADSMathSciNetGoogle Scholar
 [236]Wesselink, A. J., “Surface brightnesses in the U, B, V system with applications of M_{V} and dimensions of stars”, Mon. Not. R. Astron. Soc., 144, 297–311, (1969). [ADS]. (Cited on page 26.)ADSGoogle Scholar
 [237]Williams, L. L. R. and Saha, P., “Pixelated Lenses and H_{0} from TimeDelay Quasars”, Astron. J., 119, 439–450, (2000). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [238]WoodVasey, W. M. et al., “Observational Constraints on the Nature of Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey”, Astrophys. J., 666, 694–715, (2007). [DOI], [ADS], [arXiv:astroph/0701041]. (Cited on page 32.)ADSGoogle Scholar
 [239]Wucknitz, O., Biggs, A. D. and Browne, I. W. A., “Models for the lens and source of B0218+357: a LENSCLEAN approach to determine H_{0}”, Mon. Not. R. Astron. Soc., 349, 14–30, (2004). [DOI], [ADS]. (Cited on page 16.)ADSGoogle Scholar
 [240]York, D. G. et al., “The Sloan Digital Sky Survey: Technical Summary”, Astron. J., 120, 1579–1587, (2000). [DOI], [ADS]. (Cited on page 32.)ADSGoogle Scholar
 [241]York, T., Jackson, N., Browne, I. W. A., Wucknitz, O. and Skelton, J. E., “The Hubble constant from the gravitational lens CLASS B0218+357 using the Advanced Camera for Surveys”, Mon. Not. R. Astron. Soc., 357, 124–134, (2005). [DOI], [ADS]. (Cited on pages 14 and 15.)ADSGoogle Scholar
 [242]Zaritsky, D., Kennicutt Jr, R. C. and Huchra, J. P., “HII regions and the abundance properties of spiral galaxies”, Astrophys. J., 420, 87–109, (1994). [DOI], [ADS]. (Cited on page 26.)ADSGoogle Scholar
Copyright information
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.