Skip to main content

Part of the book series: Springer Theses ((Springer Theses))

  • 552 Accesses

Abstract

Soon after Einstein published his general theory of relativity, in order to derive a static solution out of his equations, he modified the equations by adding  Λ, the cosmological constant term [1]. This extra term could be used to explain the observations of that time that were indicating a non-evolving universe. Although Einstein may not have been aware of this fact originally, this cosmological constant can be interpreted as the vacuum energy density [2], which generates a repulsive force that can balance the attractive gravitational forces due to matter and hence grant a static, although extremely unstable, universe. The cosmological term seemed unnecessary when Hubble observed the cosmic expansion of the universe [3], and Friedmann [4] and Lemaitre [5] developed a model that could well explain the new data. Therefore, Einstein and de Sitter [6] accepted a spatially flat, matter dominated, homogeneous, isotropic, and expanding universe as the cosmological model where the matter density (ρ m ) is equal to the critical density (ρ c ), \(\Omega _m \equiv \frac {\rho _m}{\rho _c} = 1\), and there is no room for other types of energy. In the 1990s, two independent groups of cosmologists [7, 8] reported direct evidence of cosmic expansion with a positive rate from studies of supernova explosions, although other studies of the age of the universe together with cosmic microwave background (CMB) observations [9] were already indicating the shortcomings of the Einstein–de Sitter model.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Natural units are in place in this dissertation.

References

  1. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ) 1915, 844 (1915)

    Google Scholar 

  2. Y.B. Zeldovich, Sov. Phys. Uspekhi 11, 381 (1968)

    Article  ADS  Google Scholar 

  3. E. Hubble, Proc. Natl. Acad. Sci. 15, 168 (1929)

    Article  ADS  Google Scholar 

  4. A. Friedmann, On the curvature of space. Z. Phys. 10, 377 (1922)

    Article  ADS  MATH  Google Scholar 

  5. G. Lemaitre, Annales de la Societe Scietifique de Bruxelles 47, 49 (1927)

    ADS  Google Scholar 

  6. A. Einstein, W. de Sitter, Proc. Natl. Acad. Sci. 18, 213 (1932)

    Article  ADS  Google Scholar 

  7. A.G. Riess et al., [Supernova Search Team Collaboration], Astron. J. 116, 1009 (1998)

    Google Scholar 

  8. S. Perlmutter et al., [Supernova Cosmology Project Collaboration], Astrophys. J. 517, 565 (1999)

    Google Scholar 

  9. C.L. Bennett, A.J. Banday, K.M. Górski, G. Hinshaw, P. Jackson, P. Keegstra, A. Kogut, G.F. Smoot, D.T. Wilkinson, E.L. Wright, Astrophys. J. Lett. 464, L1 (1996)

    Article  ADS  Google Scholar 

  10. http://map.gsfc.nasa.gov/site/citations.html. Accessed 12 Oct 2010

  11. Planck Collaboration, Planck 2015 results. XIII. Cosmological parameters (2015) [arXiv:1502.01589]

    Google Scholar 

  12. N. Suzuki et al., [The Supernova Cosmology Project], Astrophys. J. 746, 85 (2012) [arXiv:1105.3470]

    Google Scholar 

  13. H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)

    Google Scholar 

  14. M.J. Sparnaay, Nature 180, 334 (1957)

    Article  ADS  Google Scholar 

  15. C. Wetterich, Nucl. Phys. B 302, 668 (1988)

    Article  ADS  Google Scholar 

  16. B. Ratra, P. Peebles, Phys. Rev. D 37, 3406 (1988)

    Article  ADS  Google Scholar 

  17. R. Caldwell, R. Dave, P.J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998) [arXiv:astro-ph/9708069]

    Article  ADS  Google Scholar 

  18. I. Zlatev, L.M. Wang, P.J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999) [arXiv:astro-ph/9807002]

    Article  ADS  Google Scholar 

  19. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989) [arXiv:astro-ph/0005265]

    Article  ADS  Google Scholar 

  20. R. Caldwell, E.V. Linder, Phys. Rev. Lett. 95, 141301 (2005) [arXiv:astro-ph/0505494]

    Article  ADS  Google Scholar 

  21. C. Armendariz-Picon, T. Damour, V.F. Mukhanov, Phys. Lett. B 458, 209 (1999) [arXiv:hep-th/9904075]

    Article  ADS  MathSciNet  Google Scholar 

  22. C. Armendariz-Picon, V.F. Mukhanov, P.J. Steinhardt, Phys. Rev. Lett. 85, 4438 (2000) [arXiv:astro-ph/0004134]

    Article  ADS  Google Scholar 

  23. C. Armendariz-Picon, V.F. Mukhanov, P.J. Steinhardt, Phys. Rev. D 63, 103510 (2001) [arXiv:astro-ph/0006373]

    Article  ADS  Google Scholar 

  24. E. Babichev, V.F. Mukhanov, A. Vikman, JHEP 02, 101 (2008)

    Article  ADS  Google Scholar 

  25. C. Wetterich, Astron. Astrophys. 301, 321 (1995) [arXiv:hep-th/9408025]

    ADS  Google Scholar 

  26. L. Amendola, Phys. Rev. D 62, 043511 (2000) [arXiv:astro-ph/9908023]

    Article  ADS  Google Scholar 

  27. S. Das, P.S. Corasaniti, J. Khoury, Phys. Rev. D 73, 083509 (2006) [arXiv:astro-ph/0510628]

    Article  ADS  Google Scholar 

  28. S. Capozziello, S. Carloni, A. Troisi, Recent Res. Dev. Astron. Astrophys. 1, 625 (2003) [arXiv:astro-ph/0303041]

    Google Scholar 

  29. V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, Cambridge, 2005)

    Book  MATH  Google Scholar 

  30. I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Actions in Quantum Gravity (IOP, Bristol, 1992)

    Google Scholar 

  31. A. Codello, R. Percacci, Phys. Rev. Lett. 97, 221301 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  32. T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010) [arXiv:0805.1726]

    Article  ADS  Google Scholar 

  33. G. Dvali, G. Gabadadze, M. Porrati, Phys. Lett. B 485, 208 (2000) [arXiv:hep-th/0005016]

    Article  ADS  MathSciNet  Google Scholar 

  34. S. Dubovsky, V. Rubakov, Phys. Rev. D 67, 104014 (2003) [arXiv:hep-th/0212222]

    Article  ADS  Google Scholar 

  35. C. de Rham, G. Dvali, S. Hofmann, J. Khoury, O. Pujolas et al., Phys. Rev. Lett. 100, 251603 (2008) [arXiv:0711.2072]

    Article  ADS  MathSciNet  Google Scholar 

  36. A. Nicolis, R. Rattazzi, E. Trincherini, Phys. Rev. D 79, 064036 (2009) [arXiv:0811.2197]

    Article  ADS  MathSciNet  Google Scholar 

  37. J.Q. Xia, Phys. Rev. D 79, 103527 (2009) [arXiv:0907.4860]

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Borzou, A. (2018). Dark Energy. In: Theoretical and Experimental Approaches to Dark Energy and the Cosmological Constant Problem. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-69632-4_2

Download citation

Publish with us

Policies and ethics