Abstract
The standard model of cosmology uses General Relativity (GR) to describe gravitational interactions, an homogeneous/isotropic FRW metric to describe the geometry and matter content of cold dark matter (CDM)/photons/baryons to describe its constituents. Observations of the cosmic microwave background, supernovae, baryon acoustic oscillations, gravitational lensing and structure formation point to the existence of an additional component dubbed “dark energy”, or a modification to gravity, which needs to be introduced to explain the the observed acceleration [1–5].
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References
Supernova Cosmology Project Collaboration, S. Perlmutter et al. Measurements of Omega and Lambda from 42 high redshift supernovae. Astrophys. J. 517, 565–586 (1999). [astro-ph/9812133]. The Supernova Cosmology Project
Supernova Search Team Collaboration, A. G. Riess et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998).[astro-ph/9805201]
A.G. Riess et al. BVRI light curves for 22 type Ia supernovae. Astron. J. 117, 707–724 (1999). [astro-ph/9810291]
F. Zwicky, Die Rotverschiebung von extragalaktischen Nebeln. Helv. Phys. Acta. 6, 110–127 (1933)
E. Komatsu et al. Seven-year wilkinson microwave anisotropy probe (wmap) observations: cosmological interpretation. Astrophys. J. Supplement Ser. 192(218), (2011)
C. Skordis, The tensor-vector-scalar theory and its cosmology. Class. Quant. Grav. 26, 143001 (2009). [arXiv:0903.3602]
J.D. Bekenstein, Relativistic gravitation theory for the MOND paradigm. Phys. Rev. D70, 083509 (2004). [astro-ph/0403694]
T.G. Zlosnik, P.G. Ferreira, G.D. Starkman, Modifying gravity with the Aether: an alternative to Dark Matter. Phys. Rev. D75, 044017 (2007). [astro-ph/0607411]
C. Brans, R.H. Dicke, Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925–935 (1961)
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space. Int. J. Theor. Phys. 10, 363–384 (1974)
C. Charmousis, E.J. Copeland, A. Padilla, P.M. Saffin, General second order scalar-tensor theory, self tuning, and the Fab Four. Phys. Rev. Lett. 108, 051101 (2012). [arXiv:1106.2000]
T. Kobayashi, M. Yamaguchi, J. Yokoyama, Generalized G-inflation: inflation with the most general second-order field equations. Prog. Theor. Phys. 126, 511–529 (2011). [arXiv:1105.5723]
S. Capozziello, S. Carloni, A. Troisi, Quintessence without scalar fields. Recent Res. Dev. Astron. Astrophys. 1, 625 (2003). [astro-ph/0303041]
S.M. Carroll, V. Duvvuri, M. Trodden, M.S. Turner, Is cosmic speed—up due to new gravitational physics?. Phys. Rev. D70, 043528 (2004). [astro-ph/0306438]
E.J. Copeland, M. Sami, S. Tsujikawa, Dynamics of dark energy. Int. J. Mod. Phys. D15, 1753–1936 (2006). [hep-th/0603057]
Y. Fujii, Origin of the gravitational constant and particle masses in scale invariant scalar-tensor theory. Phys. Rev. D26, 2580 (1982)
C. Armendariz-Picon, T. Damour, V.F. Mukhanov, k-Inflation. Phys. Lett. B458, 209–218 (1999). [hep-th/9904075]
C. Armendariz-Picon, V.F. Mukhanov, P.J. Steinhardt, Essentials of k essence. Phys. Rev. D63, 103510 (2001). [astro-ph/0006373]
A. Nicolis, R. Rattazzi, E. Trincherini, The Galileon as a local modification of gravity. Phys. Rev. D79, 064036 (2009). [arXiv:0811.2197]
T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Modified gravity and cosmology. Phys. Rept. 513, 1–189 (2012). [arXiv:1106.2476]
W. Hu, Structure formation with generalized dark matter. Astrophys. J.506, 485–494 (1998). [astro-ph/9801234]
J. Weller, A.M. Lewis, Large scale cosmic microwave background anisotropies and dark energy. Mon. Not. Roy. Astron. Soc. 346, 987–993 (2003). [astro-ph/0307104]
R. Bean, O. Dore, Probing dark energy perturbations: the dark energy equation of state and speed of sound as measured by WMAP. Phys. Rev. D69, 083503 (2004). [astro-ph/0307100]
W. Hu, I. Sawicki, A parameterized post-friedmann framework for modified gravity. Phys. Rev. D76, 104043 (2007). [arXiv:0708.1190]
W. Hu, Parametrized post-friedmann signatures of acceleration in the CMB. Phys. Rev. D77, 103524 (2008). [arXiv:0801.2433]
L. Amendola, M. Kunz, D. Sapone, Measuring the dark side (with weak lensing). JCAP 0804, 013 (2008). [arXiv:0704.2421]
C. Skordis, Consistent cosmological modifications to the Einstein equations. Phys. Rev. D79, 123527 (2009). [arXiv:0806.1238]
R. Bean, M. Tangmatitham, Current constraints on the cosmic growth history. Phys. Rev. D81, 083534 (2010). [arXiv:1002.4197]
L. Pogosian, A. Silvestri, K. Koyama, G.-B. Zhao, How to optimally parametrize deviations from General Relativity in the evolution of cosmological perturbations? Phys. Rev. D81, 104023 (2010). [arXiv:1002.2382]
S.A. Appleby, J. Weller, Parameterizing scalar-tensor theories for cosmological probes. JCAP 1012, 006 (2010). [arXiv:1008.2693]
A. Hojjati, L. Pogosian, G.-B. Zhao, Testing gravity with CAMB and CosmoMC. JCAP 1108, 005 (2011). [arXiv:1106.4543]
T. Baker, P.G. Ferreira, C. Skordis, J. Zuntz, Towards a fully consistent parameterization of modified gravity. Phys. Rev. D84, 124018 (2011). [arXiv:1107.0491]
T. Baker, Phi Zeta Delta: growth of perturbations in parameterized gravity for an Einstein-de Sitter Universe. Phys. Rev. D85, 044020 (2012). [arXiv:1111.3947]
C.M. Will, Theory and experiment in gravitational physics. (Cambridge University Press, Cambridge, 1993)
R.A. Battye, A. Moss, Cosmological perturbations in elastic dark energy models. Phys. Rev. D76, 023005 (2007). [astro-ph/0703744]
R.A. Battye, A. Moss, Constraints on the solid dark universe model. JCAP 0506, 001 (2005). [astro-ph/0503033]
R.A. Battye, A. Moss, Anisotropic perturbations due to dark energy. Phys. Rev. D74, 041301 (2006). [astro-ph/0602377]
R. Battye, A. Moss, Anisotropic dark energy and CMB anomalies. Phys. Rev. D80, 023531 (2009). [arXiv:0905.3403]
S. Weinberg, Effective field theory for inflation. Phys. Rev. D77, 123541 (2008). [arXiv:0804.4291]
C. Cheung, P. Creminelli, A.L. Fitzpatrick, J. Kaplan, L. Senatore, The effective field theory of inflation. JHEP 03, 014 (2008). [arXiv:0709.0293]
P. Creminelli, G. D’Amico, J. Norena, F. Vernizzi, The effective theory of Quintessence: the w¡-1 side unveiled. JCAP 0902, 018 (2009). [arXiv:0811.0827]
R. Caldwell, A. Cooray, A. Melchiorri, Constraints on a new post-general relativity cosmological parameter. Phys. Rev. D76, 023507 (2007). [astro-ph/0703375]
J.N. Dossett, M. Ishak, J. Moldenhauer, Testing general relativity at cosmological scales: implementation and parameter correlations. Phys. Rev. D84, 123001 (2011). [arXiv:1109.4583]
D. Kirk, I. Laszlo, S. Bridle, R. Bean, Optimising cosmic shear surveys to measure modifications to gravity on cosmic scales. arXiv:1109.4536
I. Laszlo, R. Bean, D. Kirk, S. Bridle, Disentangling dark energy and cosmic tests of gravity from weak lensing systematics. arXiv:1109.4535
J. Zuntz, T. Baker, P. Ferreira, C. Skordis, Ambiguous tests of general relativity on cosmological scales. JCAP 1206, 032 (2012). [arXiv:1110.3830]
T.D. Lee, A theory of spontaneous \(t\) violation. Phys. Rev. D8, 1226–1239 (1973)
B. Carter, Equations of motion of a stiff geodynamic string or higher brane. Class. Quant. Grav. 11(11), 2677 (1994)
R.A. Battye, B. Carter, Second order Lagrangian and symplectic current for gravitationally perturbed Dirac-Goto-Nambu strings and branes. Class. Quant. Grav. 17, 3325–3334 (2000). [hep-th/9811075]
B. Carter, H. Quintana, Foundations of general relativistic high-pressure elasticity theory. Proc. R. Soci. Lond. Math. Phys. Sci. 331(1584), 57–83 (1972)
B. Carter, Elastic perturbation theory in general relativity and a variation principle for a rotating solid star. Commun. Math. Phys. 30, 261–286 (1973)
B. Carter, Speed of sound in a high-pressure general-relativistic solid. Phys. Rev. D7, 1590–1593 (1973)
J.L. Friedman, B.F. Schutz, Erratum: on the stability of relativistic systems. Astrophys. J. 200, 204–220 (1975)
B. Carter, H. Quintana, Gravitational and acoustic waves in an elastic medium. Phys. Rev. D16(1016), 2928–2938 (1977)
B. Carter, Rheometric structure theory, convective differentiation and continuum electrodynamics. Proc. R. Soci. Lond. Math. Phys. Sci. 372(1749), 169–200 (1980)
L.D. Landau, E.M. Lifshitz, Theory of Elasticity, 3rd edn. (Pergamon Press, Oxford, 1986)
M. Bucher, D.N. Spergel, Is the dark matter a solid?. Phys. Rev. D60, 043505 (1999). [astro-ph/9812022]
B. Carter, Interaction of gravitational waves with an elastic solid medium. gr-qc/0102113
T. Azeyanagi, M. Fukuma, H. Kawai, K. Yoshida, Universal description of viscoelasticity with foliation preserving diffeomorphisms. Phys. Lett. B681, 290–295 (2009). [arXiv:0907.0656]
M. Fukuma, Y. Sakatani, Relativistic viscoelastic fluid mechanics. Phys. Rev. E84, 026316 (2011). [arXiv:1104.1416]
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Pearson, J. (2014). The Effective Action Formalism for Cosmological Perturbations. In: Generalized Perturbations in Modified Gravity and Dark Energy. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01210-0_2
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