Abstract
This chapter introduces the observational data on the structure, composition, and evolution of the Universe, within the framework of the theory of general relativity, and describes the model currently providing the best quantitative description. In particular, we will illustrate the experimental evidence suggesting the existence of new forms of matter of energy, and describe the expansion, the chemical evolution, and the formation of structures, from the beginning of time—that, we believe, started with a phase transition from a singularity: the “big bang”.
This chapter introduces the observational data on the structure, composition, and evolution of the Universe, within the framework of the theory of general relativity, and describes the model currently providing the best quantitative description. In particular, we will illustrate the experimental evidence suggesting the existence of new forms of matter of energy, and describe the expansion, the chemical evolution, and the formation of structures, from the beginning of time—that, we believe, started with a phase transition from a singularity: the “big bang”.
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Notes
- 1.
Cepheids are variable red supergiant stars with pulsing periods strongly correlated with their absolute luminosity. This extremely useful propriety was discovered by the US astronomer Henrietta Leavitt at the beginning of twentieth century and has been used by Hubble to demonstrate in 1924 that the Andromeda Nebula M31 was too far to be part of our own galaxy, the Milky Way.
- 2.
The Supernova Cosmology Project is a collaboration, led by Saul Perlmutter , dedicated to the study of distant supernovae of type Ia, that started collecting data in 1988. Another collaboration also searching for distant supernovae of type Ia was formed by Brian Schmidt Adam Riess in 1994, the High-z Supernova Search Team. These teams found over 50 distant supernovae of type Ia for which the light received was weaker than expected—which implied that the rate of expansion of the Universe was increasing. Saul Perlmutter, born in 1959 in Champaign–Urbana, IL, USA, Ph.D. from University of California, Berkeley; Brian P. Schmidt, U.S. and Australian citizen, born in 1967 in USA, Ph.D. from Harvard; Adam G. Riess, born in 1969 in Washington, DC, USA. Ph.D. from Harvard, all professors in the US, were awarded the 2011 Nobel Prize in Physics “for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.”
- 3.
Arno Penzias (1933–) was born in Munich, Germany. In 1939 his family was rounded up for deportation, but they managed to escape to the US, where he could graduate in Physics at Columbia University. Robert Wilson (1936–) grew up in Huston, Texas, and studied at Caltech. They shared the 1978 Nobel prize in Physics “for their discovery of the cosmic microwave background radiation.”
- 4.
Three satellite missions have been launched so far to study the cosmic background radiation. The first was COBE in 1989 , followed by WMAP (Wilkinson Microwave Anisotropy Probe) in 2001, both of which were NASA missions. The latest (with the best angular resolution and sensitivity), called Planck , has been launched by the European Space Agency (ESA) with a contribution from NASA in 2009, and is still in orbit. In terms of sensitivity and angular resolution, WMAP improved COBE by a factor of 40, and Planck gave a further improvement by a factor of 4; in addition Planck measures polarization. The instruments onboard Planck are a low frequency (solid state) instrument from 30 GHz, and a bolometer—a device for measuring the power of incident electromagnetic radiation via the heating of a material with a temperature-dependent electrical resistance—for higher frequencies (up to 900 GHz). The total weight of the payload is 2 tons (it is thus classified as a large mission); it needs to be kept at cryostatic temperatures. John Mather , from the Goddard Space Flight Center, and George Smoot , at the University of California, Berkeley, shared the 2006 Nobel Prize in Physics “for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation”.
- 5.
Iron (\(^{56}\)Fe) is the stable element for which the binding energy per nucleon is largest (about 8.8 MeV); it is thus the natural endpoint of fusion processes of lighter elements, and of fission of heavier elements.
- 6.
The word virial comes from the latin vis, i.e., strength, or force; the term was coined by German physicist and mathematician Rudolf Clausius, one of the founders of the science of thermodynamics, around 1870.
- 7.
In the neighborood of the Solar System one has a DM density
$$\begin{aligned} \rho _{\mathrm{DM,local}} \simeq 0.4 \, \mathrm {GeV/cm^3} \, , \end{aligned}$$i.e., five orders of magnitude larger than the total energy density of the Universe.
- 8.
r is dimensionless, with range [0, 1]; \(\mathrm{K}\) is the curvature, which, in general, can be \(-1\), 0, or \(+1\). The more general change of coordinates \(r'=a \sin \theta \) does not result in anything new, and can be recast in the form used above after setting \(r = r' / a\). Of course with the \(r'\) coordinate, the curvature is not normalized, and can be, generically, negative, zero, or positive.
- 9.
From astrophysical observations the local WIMP density about 0.4 GeV/cm\(^3\); the velocity distribution is maxwellian, truncated by the galactic escape velocity of 650 km/s. For a mass of 50 GeV, the RMS velocity is comparable to the speed of the solar system in the galaxy, \(\sim \) 230 km/s.
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Appendices
Further Reading
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[F8.1]
J. Silk, “The big bang”, Times Books 2000.
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[F8.2]
B. Ryden, “Introduction to Cosmology”, Addison Wesley, Pearson Education 2003. This book provides a clear introduction to cosmology for upper level undergraduates.
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[F8.3]
E.F. Taylor and J.A. Wheeler, “Exploring Black Holes, introduction to general relativity”, Addison Wesley 2000. This book provides an enlightening introduction to the physics of black holes emphasizing how they are “seen” by observers in different reference frames.
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[F8.4]
M.V. Berry, “Principles of Cosmology and Gravitation”, Adam Hilger 1989. This book presents the fundamentals of general relativity and cosmology with many worked examples and exercises without requiring the use of tensor calculus.
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[F8.5]
V. Mukhanov, “Physical Foundations of Cosmology”, Cambridge 2005. This book provides a comprehensive introduction to inflationary cosmology at early graduate level.
Exercises
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1.
Cosmological principle and Hubble law. Show that the Hubble law does not contradict the cosmological principle (all points in space and time are equivalent).
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2.
Olbers Paradox. Why is the night dark? Does the existence of interstellar dust (explanation studied by Olbers himself) solve the paradox?
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3.
Steady state Universe. In a steady state Universe with Hubble law, matter has to be permanently created. Compute in that scenario the creation rate of matter.
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4.
Blackbody form of the Cosmic Microwave Background. In 1965 Penzias and Wilson discovered that nowadays the Universe is filled with a cosmic microwave background which follows an almost perfect Planck blackbody formula. Show that the blackbody form of the energy density of the background photons was preserved during the expansion and the cooling that had occurred in the Universe after photon decoupling.
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5.
Nucleosynthesis and neutron lifetime. The value of the neutron lifetime, which is anormaly long for weak decay processes (why?), is determinant in the evolution of the Universe. Discuss what would have been the primordial fraction of He if the neutron lifetime would have been one-tenth of its real value.
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6.
GPS time corrections. Identical clocks situated in a GPS satellite and at the Earth surface have different periods due general relativity effects. Compute the time difference in one day between a clock situated in a satellite in a circular orbit around Earth with a period of 12 h and a clock situated on the Equator at the Earth surface. Consider that Earth has a spherical symmetry and use the Schwarzschild metric.
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7.
Asymptotically Matter-dominated Universe. Consider a Universe composed only by matter and radiation. Show that whatever would have been the initial proportion of the matter and the radiation energy densities this Universe will be asymptotically matter dominated.
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8.
Flatness of the Early Universe. The present experimental data indicate a value for a total energy density of the Universe compatible with one within a few per mil. Compute the maximum possible value of \(|\Omega -1|\) at the scale of the electroweak symmetry breaking consistent with the measurements at the present time.
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9.
WIMP “miracle”. Show that a possible Weak Interacting Massive Particle (WIMP) with a mass of the order of \(m_\chi \) \(\sim \) 100 GeV would have the relic density needed to be the cosmic dark matter (this is the so-called WIMP “miracle”).
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De Angelis, A., Pimenta, M.J.M. (2015). The Standard Model of Cosmology and the Dark Universe. In: Introduction to Particle and Astroparticle Physics. Undergraduate Lecture Notes in Physics. Springer, Milano. https://doi.org/10.1007/978-88-470-2688-9_8
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