Skip to main content
SpringerLink
Log in

The Standard Cosmological Model: Achievements and Issues

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The present day standard cosmological model is a great theoretical achievement. This chapter surveys the main themes that have arisen and issues that are still oustanding.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. The original motivation for inflation [50] was actually philosophical [53]. It is its role in structure formation that makes it physics.

  2. Unless the dark energy decays in the future, when a variety of options will open; but there is no solid reason to believe this will happen.

  3. See a comment on this as regards inflation by Sabine Hossenfelder [53]

  4. Some alleged inflationary singularity theorems may be correct mathematically but they exclude non-singular bouncing models such as the \(k=+1\) de Sittermodel by fiat.

  5. Discussions with Ashtekhar, Unruh, and Wald.

References

  1. Ade. et al.: Ast Ast Planck 2013 results. XVI. Cosmological parameters. 571, A16 (2014). [arXiv:1303.5076]

  2. Ade et al.: Planck 2015 results. XIII. Cosmological parameters. Ast and Ast. 594, A13 (2015) [arXiv:1502.01589]

  3. Aguirre, A.: On making predictions in a multiverse: Conundrums, dangers, and coincidences. In: Carr, B. (ed.), Universe or multiverse. Cambridge University Press, Cambridge p. 22 (2005) (arXiv:astro-ph/0506519)

  4. Albert, D.Z.: Time and Chance. Harvard University Press, Cambridge (2003)

    Google Scholar 

  5. Albrecht, A. et al.: Report of the dark energy task force. (2006) arXiv:astro-ph/0609591

  6. Bardeen, J.: Gauge-invariant cosmological perturbations. Phys. Rev. D 22, 1882–1905 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  7. Barrow, J., Tipler, F.: The Cosmological Anthropic Principle. Oxford University Press, Oxford (1984)

    Google Scholar 

  8. Bartelmann, M., Schneider, P.: Weak gravitational lensing. Phys. Rep. 340, 291–472 (2001)

    Article  ADS  Google Scholar 

  9. Bernal, J.L., Verde, L., Riess, A.G.: The trouble with \(H\_0\). J. Cosmol. Astropart. Phys. 10, 019 (2016)

    Article  ADS  Google Scholar 

  10. Bertone, G., Hooper, D., Silk, J.: Particle dark matter: evidence, candidates and constraints. Phys. Rep. 405, 279–390 (2005)

    Article  ADS  Google Scholar 

  11. Betoule, M., et al.: Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples. Astron. Astrophys. 568, A22 (2014)

    Article  Google Scholar 

  12. Bondi, H.: Spherically symmetrical models in general relativity. Mon. Not. R. Ast. Soc. 107, 410–425 (1947). Reprinted as Gen Ral Grav 31, 1777-1781 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  13. Bondi, H.: Cosmology. Cambridge University Press, Cambridge (1960)

    MATH  Google Scholar 

  14. Carr, B.J. (ed.): Universe or Multiverse?. CambridgeUniversity Press, Cambridge (2009)

    MATH  Google Scholar 

  15. Célérier, M.-N.: The accelerated expansion of the universe challenged by an effect of the inhomogeneities. In: A Review. New Advances in Physics 1, 29 (2007). [arXiv:astro-ph/0702416]

  16. Challinor, A.: Microwave background anisotropies from gravitational waves: the 1 + 3 covariant approach. Class. Quant. Grav. 17, 871–889 (2000). [arXiv:astro-ph/9906474]

    Article  ADS  MathSciNet  Google Scholar 

  17. Challinor, A.D., Lasenby, A.N.: A covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations. Phys. Rev. D58, 023001 (1998). [arXiv:astro-ph/9804150]

    ADS  Google Scholar 

  18. Challinor, A., Lasenby, A.: Cosmic microwave background anisotropies in the CDM model: a covariant and gauge-invariant approach. Astrophys. J. 513, 1–22 (1999). [arXiv:astro-ph/9804301]

    Article  ADS  Google Scholar 

  19. Clarkson, C., Maartens, R.: Inhomogeneity and the foundations of concordance cosmology. Class. Quant. Grav. 27, 124008 (2010). [arXiv:1005.2165]

    Article  ADS  MathSciNet  Google Scholar 

  20. Clifton, T., Ferreira, P.G., Padilla, A., Skordi, C.: Modified gravity and cosmology. Phys. Rep. 513, 1–189 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  21. Cooray, A.: Extragalactic background light: measurements and applications. (2016) arXiv:1602.03512

    Article  Google Scholar 

  22. Cornish, N.J., Spergel, D.N., Starkman, G.D., Komatsu, E.: Constraining the topology of the universe. Phys. Rev. Lett. 92, 201302 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  23. Delubac, T., et al.: Baryon acoustic oscillations in the Ly-\(\alpha \) forest of BOSS DR11 quasars. Astron. Astrophys. 574, A59 (2015)

    Article  Google Scholar 

  24. Dodelson, S.: Modern Cosmology. Academic Press, Cambridge (2003)

    Google Scholar 

  25. Durrer, R.: The Cosmic Microwave Background. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  26. Ehlers, J.: Contributions to the Relativistic Mechanics of Continuous Media. Akademie der Wissenschaften und Literatur (Mainz), Abhandlungen der Mathematisch-Naturwissenschaftlichen Klasse 11, 792-837 (1961). Reprinted as Golden Oldie: Gen. Rel. Grav. 25, 1225-66 (1993)

  27. Ehlers, J., Geren, P., Sachs, R.K.: Isotropic solutions of the Einstein-Liouville equations. J. Math. Phys. 9, 1344 (1968)

    Article  ADS  Google Scholar 

  28. Ehlers, J., Rindler, W.: A phase-space representation of Friedmann–Lemaître universes containing both dust and radiation and the inevitability of a big bang. Mon. Not. R. Ast. Soc. 238, 503–521 (1989)

    Article  ADS  Google Scholar 

  29. Einstein, A.: Kosmologische Betrachtungen zur Allgemeinen Relativitatstheorie, pp. 142–152. Preussische Akademie der Wissenschaften, Berlin (1917)

    MATH  Google Scholar 

  30. Ellis, G.F.R.: General relativity and cosmology. In: General Relativity and Cosmology, Varenna Course No. XLVII, Sachs, R.K. (ed). (Academic, New York) (1971). Reprinted as Golden Oldie, General Relativity and Gravitation. 41, 581–660 (2009)

  31. Ellis, G.F.R.: Topology and cosmology. Gen. Relat. Gravit. 2, 7–21 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  32. Ellis, G.F.R., et al.: Innovation, resistance and change: the transition to the expanding universe. In: Bertotti, B., et al. (eds.) Modern Cosmology in Retrospect. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  33. Ellis, G.F.R.: Editorial note to: E. Lifshitz, on the gravitational stability of the expanding universe. Gen. Relat. Gravit. 49, 17 (2017)

    Article  ADS  Google Scholar 

  34. Ellis, G.F.R., Bruni, M.: Covariant and gauge-invariant approach to cosmological density fluctuations. Phys. Rev. D 40, 1804 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  35. Ellis, G.F.R., Hwang, J., Bruni, M.: Covariant and gauge-independent perfect-fluid Robertson–Walker perturbations. Phys. Rev. D 40, 1819 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  36. Ellis, G.F.R., Maartens, R.: The emergent universe: inflationary cosmology with no singularity. Class. Quantum Gravity 21, 22332 (2004). [arXiv:grqc/0211082]

    MathSciNet  MATH  Google Scholar 

  37. Ellis, G.F.R., Maartens, R., MacCallum, M.A.H.: Relativistic Cosmology. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  38. Ellis, G.F.R., Nel, S.D., Maartens, R., Stoeger, W.R., Whitman, A.P.: Ideal observational cosmology. Phys. Rep. 124, 315–417 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  39. Ellis, G.F.R., Madsen, M.: Exact scalar field cosmologies. Class. Quantum Gravity 8, 667–676 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  40. Ellis, G.F.R., van Elst, H., Murugan, J., Uzan, J.-P.: On the trace-free Einstein equations as a viable alternative to general relativity. Class. Quantum Gravity 28, 225007 (2011). [arXiv:1008.1196]

    Article  ADS  MathSciNet  Google Scholar 

  41. Ellis, G.F.R., Platts, E., Sloan, D., Weltman, A.: Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology. JCAP 2016, 4 (2016)

    Google Scholar 

  42. Ellis, G.F.R., Schreiber, G.: Observational and dynamical properties of small universes. Phys. Lett. A 115, 97–107 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  43. Ellis, G., Silk, J.: Defend the integrity of physics. Nature 516, 321–323 (2014)

    Article  ADS  Google Scholar 

  44. Ellis, G., Uzan, J.-P.: Inflation and the Higgs particle. Astrono. Geophys. 55, 1.191.20 (2014)

    Google Scholar 

  45. Ellis, G.F.R., Uzan, J.P.: Causal structures in inflation. Comptes Rendus Phys. 16, 928–947 (2015)

    Article  ADS  Google Scholar 

  46. February, S., Larena, J., Smith, M., Clarkson, C.: Rendering dark energy void. Mon. Not. R. Astron. Soc. 405, 2010 (2010). [arXiv:0909.1479v2]

    Google Scholar 

  47. Friedmann, A.: Über die Krümmung des Raumes. Z. Phys. 10, 377 (1922)

    Article  ADS  Google Scholar 

  48. Friedmann, A.: Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes. Z. Phys. 21, 326–332 (1924)

    Article  ADS  MathSciNet  Google Scholar 

  49. Greene, B.: The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos. Knopf, New York (2007)

    MATH  Google Scholar 

  50. Guth, A.H.: Inflationary universe: a possible solution to the horizon and flatness problems. Phys. Rev. D 23, 347?56 (1981)

    ADS  MATH  Google Scholar 

  51. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)

    Book  Google Scholar 

  52. Hilbert, D.: On the infinite. Math. Ann. 95, 161–190 (1926). Reprinted in Philosophy of mathematics: Selected readings (eds.) Benacerraf, P., Putnam, H. (Cmabridge University Press ) Hilbert

    Article  MathSciNet  Google Scholar 

  53. Hossenfelder, S.: Is The Inflationary Universe A Scientific Theory? Not Anymore. Starts with a Bang 2017/09/28: webpage here (2017)

  54. Kamionkowski, M., Loeb, A.: Getting around cosmic variance. Phys. Rev. D 56, 4511 (1997)

    Article  ADS  Google Scholar 

  55. Kristian, J., Sachs, R.K.: Observations in cosmology. Astrophys. J. 399, 143–379 (1966). Reprinted as GRG Golden Oldie: Gen. Rel. Grav. 43, 337-58 (2011)

    MathSciNet  Google Scholar 

  56. Lachieze-Rey, M., Luminet, J.-P.: Cosmic topology. Phys. Rep. 254, 135–214 (1995). arXiv:gr-qc/9605010

    Article  ADS  MathSciNet  Google Scholar 

  57. Lemaïtre, G.: A homogeneous universe of constant mass and increasing radius accounting for the R: (1927), 4959. Published in translation in MNRAS 91 (1931) 483–90, and republished as GRG Golden Oldie. General Relativity and Gravitation, 45(2013), 1635–1646

  58. Lemaïtre, G.: The Primeval Atom: An Essay on Cosmogony. D. Van Nostrand and Co, Princeton (1951)

    Google Scholar 

  59. Lewis, A., Challinor, A., Lasenby, A.: Efficient computation of cosmic microwave background anisotropies in closed Friedmann–Robertson–Walker models. Astrophys. J. 538, 473–476 (2000)

    Article  ADS  Google Scholar 

  60. Lidsey, J.E., Liddle, A.R., Kolb, E.W., Copeland, E.J., Barreiro, T., Abney, M.: Reconstructing the inflaton potential: an overview. Rev. Mod. Phys. 69, 373–410 (1997)

    Article  ADS  Google Scholar 

  61. Luminet, J.-P.: The status of cosmic topology after planck data. (2016) arXiv:1601.03884v2

  62. Maartens, R.: Is the Universe homogeneous? Philos. Trans. R. Soc A 369, 5115–5137 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  63. Marra, V., Amendola, L., Sawicki, I., Valkenburg, W.: Cosmic variance and the measurement of the local Hubble parameter. Phys. Rev. Lett. 110, 241305 (2013)

    Article  ADS  Google Scholar 

  64. Martin, J., Ringeval, C., Vennin, V.: Encyclopaedia inflationaris. Phys. Dark Univ. 5–6, 75–235 (2014). [arXiv:1303.3787]

    Article  Google Scholar 

  65. Mukhanov, V.: Physical Foundations of Cosmology. Cambridge University Press, Cambridg (2005)

    Book  Google Scholar 

  66. Mukhanov, V.F., Feldman, H.A., Brandenberger, R.H.: Theory of cosmological perturbations. Phys. Rep. 215, 203–333 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  67. Mustapha, N., Hellaby, C., Ellis, G.F.R.: Large scale inhomogeneity versus source evolution: can we distinguish them observationally? Mon. Not. R. Astrron. Soc. 292, 817–830 (1997). arXiv:gr-qc/9808079

    Article  ADS  Google Scholar 

  68. Particle Data Group., Lahav, O., Liddle, A.R.: The cosmological parameters. http://pdg.lbl.gov/2015/reviews/rpp2015-rev-cosmological-parameters.pdf

  69. Peebles, P.J.E.: The Large-Scale Structure of the Universe. Princeton University Press, Princeton (1980)

    Google Scholar 

  70. Peebles, P.J.E., Yu, J.T.: Primeval adiabatic perturbation in an expanding universe. Astrophys. J. 162, 81536 (1970)

    Article  Google Scholar 

  71. Penrose, R.: Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14, 579–581 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  72. Penrose, R.: Difficulties with Inflationary Cosmology. Annals of the New York Academy of Sciences. vol. 571. Texas Symposium on Relativistic Astrophysics. pp. 249–264 (1989)

    Article  ADS  Google Scholar 

  73. Penrose, R.: Fashion Faith and Fantasy in the New Phyiscs of the UnIverse. Princeton University Press, Princeton (2016)

    Book  Google Scholar 

  74. Peter, P., Uzan, J.-P.: Primordial Cosmology. Oxford Graduate Texts, Oxford (2013)

    Google Scholar 

  75. Rees, M.J.: Just Six Numbers: The Deep Forces that Shape the Universe. Weidenfeld and Nicholson, London (1999)

    MATH  Google Scholar 

  76. Rees, M.J.: Our Cosmic Habitat. Princeton University Press, Princeton (2001)

    Google Scholar 

  77. Rindler, W.: Visual horizons in world models. Mon. Not. R. Astron. Soc. 116, 662–677 (1956). Reprinted as Golden Oldie: Gen Rel Grav. 34, 133 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  78. Robertson, H.P.: Relativistic cosmology. Rev. Mod. Phys. 5, 62–90 (1933). Reprinted as Golden Oldie Gen. Rel. Grav. 44, 2115-44 (2012)

    Article  ADS  Google Scholar 

  79. Rovelli, C.: The dangers of non-empirical confirmation. (2016) arXiv preprint arXiv:1609.01966

  80. Sachs, R.K., Wolfe, A.M.: Perturbations of a cosmological model and angular variations of the microwave background. Astrophys. J. 147, 73–89 (1967). Reprinted as GRG Golden Oldie: Gen. Rel. Grav. 39, 1944 (2007)

    Article  ADS  Google Scholar 

  81. Sandage, A.: The ability of the 200-inch telescope to discriminate between selected world models. Astrophys. J. 133, 355–392 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  82. Steigman, G.: Primordial nucleosynthesis in the precision cosmology era. Annu. Rev. Nucl. Part. Sci. 57, 463–491 (2007)

    Article  ADS  Google Scholar 

  83. Tegmark, M., et al.: Cosmological constraints from the SDSS luminous red galaxies. Phys. Rev. D 74, 123507 (2006)

    Article  ADS  Google Scholar 

  84. Tolman, R.C.: Relativity, Thermodynamics, and Cosmology. Clarendon Press, Oxford (1934)

    MATH  Google Scholar 

  85. Uzan, J.-P.: The big-bang theory: construction, evolution and status. In: Introductory lecture notes from the Poincaré seminar XX (2015) and Les Houches school Cosmology after Planck: what is next? (2016). Available at arXiv:1606.06112 (2016)

  86. Wagner, A.: Arrival of the Fittest. Penguin Random House, New York (2017)

    Google Scholar 

  87. Weinberg, S.: Living in the multiverse. In: Carr, B. (ed.) Universe or Multiverse?. Cambridge University Press, Cambridge (2007). arXiv:hep-th/0511037

    Google Scholar 

  88. Zhang, P., Stebbins, A.: Confirmation of the Copernican principle through the anisotropic kinetic Sunyaev Zel’dovich effect. Phil. Trans. R. Soc. A 369, 5138–5145 (2011)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Cape Town, Rondebosch, Cape Town, South Africa

    George Ellis

Authors
  1. George Ellis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George Ellis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ellis, G. The Standard Cosmological Model: Achievements and Issues. Found Phys 48, 1226–1245 (2018). https://doi.org/10.1007/s10701-018-0176-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-018-0176-x

Keywords

Search

Navigation