Skip to main content
SpringerLink
Log in

The cosmological constant

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

The energy density of the vacuum, Λ, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Λ = 0 conflicts with observation. The possibility remains that Λ is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.

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

Similar content being viewed by others

References

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

    Google Scholar 

  2. Gibbons, G.W., Hawking, S.W.: Cosmological event horizons, thermodynamics, and particle creation. Phys. Rev. D 15, 2738 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  3. Edwards, D.: Exact expressions for the properties of the zero-pressure Friedmann models. M.N.R.A.S. 159, 51 (1972)

    ADS  Google Scholar 

  4. Polchinski, J.: The cosmological constant and the string landscape. (2006), hep-th/0603249

  5. Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys. 61, 1 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  6. Carroll, S.M.: The cosmological constant, astro-ph/0004075

  7. Bousso, R.: Precision cosmology and the landscape. (2006), hep-th/0610211

  8. Dyson, L., Kleban, M., Susskind, L.: Disturbing implications of a cosmological constant. JHEP 10, 011 (2002), hep-th/0208013

  9. Banks, T.: Entropy and initial conditions in cosmology. (2007), hep-th/0701146

  10. Linde, A.D.: The inflationary universe. Rept. Prog. Phys. 47, 925 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  11. Sakharov, A.D.: Cosmological transitions with a change in metric signature. Sov. Phys. JETP 60, 214 (1984)

    Google Scholar 

  12. Banks, T.: T C P, quantum gravity, the cosmological constant and all that. Nucl. Phys. B 249, 332 (1985)

    Article  ADS  Google Scholar 

  13. Linde, A.: Inflation and quantum cosmology. In: Hawking, S.W., Israel, W.(eds) 300 Years of Gravitation, pp. 604–630. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  14. Weinberg, S.: Anthropic bound on the cosmological constant. Phys. Rev. Lett. 59, 2607 (1987)

    Article  ADS  Google Scholar 

  15. Davies, P.C.W., Unwin, S.D.: Why is the cosmological constant so small. Proc. R. Soc. Lond. A 377, 147 (1982)

    ADS  MathSciNet  Google Scholar 

  16. Barrow, J.D., Tipler, F.J.: The Anthropic Cosmological Principle. Clarendon Press, Oxford (1986)

    Google Scholar 

  17. Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998), astro-ph/9805201

    Google Scholar 

  18. Perlmutter, S., et al.: Measurements of Omega and Lambda from 42 high-redshift supernovae. Astrophys. J. 517, 565 (1999), astro-ph/9812133

    Google Scholar 

  19. Tegmark, M., et al.: Cosmological constraints from the SDSS luminous red galaxies. Phys. Rev. D 74, 123507 (2006), astro-ph/0608632

    Google Scholar 

  20. Albrecht, A., et al.: Report of the Dark Energy Task Force. (2006), astro-ph/0609591

  21. Brown, J.D., Teitelboim, C.: Dynamical neutralization of the cosmological constant. Phys. Lett. B 195, 177 (1987)

    Article  ADS  Google Scholar 

  22. Brown, J.D., Teitelboim, C.: Neutralization of the cosmological constant by membrane creation. Nucl. Phys. B 297, 787 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  23. Abbott, L.F.: A mechanism for reducing the value of the cosmological constant. Phys. Lett. B 150, 427 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  24. Duff, M.J., Nieuwenhuizen, P.: Quantum inequivalence of different field representations. Phys. Lett. B 94, 179 (1980)

    Article  ADS  Google Scholar 

  25. Aurilia, A., Nicolai, H., Townsend, P.K.: Hidden constants: The theta parameter of QCD and the cosmological constant of N=8 supergravity. Nucl. Phys. B 176, 509 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  26. Bousso, R., Polchinski, J.: Quantization of four-form fluxes and dynamical neutralization of the cosmological constant. JHEP 06, 006 (2000), hep-th/0004134

    Google Scholar 

  27. Steinhardt, P.J., Turok, N.: Why the cosmological constant is small and positive. Science 312, 1180 (2006), astro-ph/0605173

    Google Scholar 

  28. Hawking, S.W.: The cosmological constant is probably zero. Phys. Lett. B 134, 403 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  29. Klebanov, I.R., Susskind, L., Banks, T.: Wormholes and the cosmological constant. Nucl. Phys. B 317, 665 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  30. Coleman, S.: Why there is nothing rather than something: A theory of the cosmological constant. Nucl. Phys. B 310, 643 (1988)

    Article  ADS  Google Scholar 

  31. Coleman, S., Luccia, F.D.: Gravitational effects on and of vacuum decay. Phys. Rev. D 21, 3305 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  32. Guth, A.H., Weinberg, E.J.: Could the universe have recovered from a slow first-order phase transition?. Nucl. Phys. B 212, 321 (1983)

    Article  ADS  Google Scholar 

  33. Dasgupta, K., Rajesh, G., Sethi, S.: M theory, orientifolds and g-flux. JHEP 08, 023 (1999), hep-th/9908088

    Google Scholar 

  34. Giddings, S.B., Kachru, S., Polchinski, J.: Hierarchies from fluxes in string compactifications. Phys. Rev. D 66, 106006 (2002), hep-th/0105097

    Google Scholar 

  35. Silverstein, E.: TASI / PiTP / ISS lectures on moduli and microphysics. (2004), hep-th/0405068

  36. Grana, M.: Flux compactifications in string theory: A comprehensive review. Phys. Rept. 423, 91 (2006), hep-th/0509003

    Google Scholar 

  37. Douglas, M.R., Kachru, S.: Flux compactification. (2006), hep-th/0610102

  38. Kachru, S., Kallosh, R., Linde A., Trivedi, S.P.: De Sitter vacua in string theory. Phys. Rev. D 68, 046005 (2003), hep-th/0301240

    Google Scholar 

  39. Silverstein, E.: (A)dS backgrounds from asymmetric orientifolds. (2001), hep-th/0106209

  40. Maloney, A., Silverstein, E., Strominger, A.: De Sitter space in noncritical string theory. (2002), hep-th/0205316

  41. Denef, F., Douglas, M.R.: Distributions of flux vacua. JHEP 05, 072 (2004), hep-th/0404116

  42. Farhi, E., Guth, A.H.: An obstacle to creating a universe in the laboratory. Phys. Lett. B 183, 149 (1987)

    Article  ADS  Google Scholar 

  43. Page, D.N.: Typicality defended. (2007), arXiv:0707.4169 [hep-th]

  44. Douglas, M.R.: The statistics of string / M theory vacua. JHEP 05, 046 (2003), hep-th/0303194

  45. Gmeiner, F., Blumenhagen, R., Honecker, G., Lust, D., Weigand, T.: One in a billion: MSSM-like D-brane statistics. JHEP 01, 004 (2006), hep-th/0510170

    Google Scholar 

  46. Douglas, M.R., Taylor, W.: The landscape of intersecting brane models. JHEP 01, 031 (2007), hep-th/0606109

  47. Kumar, J.: A review of distributions on the string landscape. Int. J. Mod. Phys. A21, 3441 (2006), hep-th/0601053

  48. Vafa, C.: The string landscape and the swampland. (2005), hep-th/0509212

  49. Arkani-Hamed, N., Motl, L., Nicolis, A., Vafa, C.: The string landscape, black holes and gravity as the weakest force. JHEP 06, 060 (2007), hep-th/0601001

    Google Scholar 

  50. Ooguri, H., Vafa, C.: On the geometry of the string landscape and the swampland. Nucl. Phys. B766, 21 (2007), hep-th/0605264

  51. Linde, A., Linde, D., Mezhlumian, A.: From the big bang theory to the theory of a stationary universe. Phys. Rev. D 49, 1783 (1994), gr-qc/9306035

    Google Scholar 

  52. García-Bellido, J., Linde, A., Linde, D.: Fluctuations of the gravitational constant in the inflationary Brans–Dicke cosmology. Phys. Rev. D 50, 730 (1994), astro-ph/9312039

    Google Scholar 

  53. Garriga, J., Vilenkin, A.: A prescription for probabilities in eternal inflation. Phys. Rev. D 64, 023507 (2001), gr-qc/0102090

    Google Scholar 

  54. Garriga, J., Schwartz-Perlov, D., Vilenkin, A., Winitzki, S.: Probabilities in the inflationary multiverse. JCAP 0601, 017 (2006), hep-th/0509184

    Google Scholar 

  55. Easther, R., Lim, E.A., Martin, M.R.: Counting pockets with world lines in eternal inflation (2005), astro-ph/0511233

  56. Linde, A.: Sinks in the landscape, Boltzmann Brains, and the cosmological constant problem. JCAP 0701, 022 (2007), hep-th/0611043

    Google Scholar 

  57. Vanchurin, V.: Geodesic measures of the landscape. Phys. Rev. D 75, 023524 (2007), hep-th/0612215

  58. Bousso, R.: Holographic probabilities in eternal inflation. Phys. Rev. Lett. 97, 191302 (2006), hep-th/0605263

    Google Scholar 

  59. Bousso, R., Freivogel, B., Yang, I.-S.: Eternal inflation: The inside story. Phys. Rev. D 74, 103516 (2006), hep-th/0606114

    Google Scholar 

  60. Freivogel, B., Susskind, L.: A framework for the landscape. (2004), hep-th/0408133

  61. Feldstein, B., Hall, L.J., Watari, T.: Density perturbations and the cosmological constant from inflationary landscapes. Phys. Rev. D 72, 123506 (2005), hep-th/0506235

    Google Scholar 

  62. Garriga, J., Vilenkin, A.: Anthropic prediction for Lambda and the Q catastrophe. Prog. Theor. Phys. Suppl. 163, 245 (2006), hep-th/0508005

    Google Scholar 

  63. Page, D.N.: Is our universe likely to decay within 20 billion years? (2006), hep-th/0610079

  64. Bousso, R., Freivogel, B.: A paradox in the global description of the multiverse. JHEP 06, 018 (2007), hep-th/0610132

    Google Scholar 

  65. Schwartz-Perlov, D., Vilenkin, A.: Probabilities in the Bousso-Polchinski multiverse. JCAP 0606, 010 (2006), hep-th/0601162

  66. Linde, A.: Towards a gauge invariant volume-weighted probability measure for eternal inflation. JCAP 0706, 017 (2007), arXiv:0705.1160 [hep-th]

  67. Bousso, R., Yang, I.-S.: Landscape predictions from cosmological vacuum selection. Phys. Rev. D 75, 123520 (2007), hep-th/0703206

    Google Scholar 

  68. Olum, K.D., Schwartz-Perlov, D.: Anthropic prediction in a large toy landscape (2007), arXiv:0705.2562 [hep-th]

  69. Clifton, T., Shenker, S., Sivanandam, N.: Volume weighted measures of eternal inflation in the Bousso-Polchinski landscape (2007), arXiv:0706.3201 [hep-th]

  70. Bousso, R.: The holographic principle. Rev. Mod. Phys. 74, 825 (2002), hep-th/0203101

  71. Efstathiou, G.P.: M.N.R.A.S. 274, L73 (1995)

    ADS  Google Scholar 

  72. Vilenkin, A.: Quantum cosmology and the constants of nature. gr-qc/9512031

  73. Weinberg, S.: Theories of the cosmological constant. astro-ph/9610044

  74. Martel, H., Shapiro, P.R., Weinberg, S.: Likely values of the cosmological constant. astro-ph/9701099

  75. Vilenkin, A.: Anthropic predictions: the case of the cosmological constant (2004), astro-ph/0407586

  76. Weinberg, S.: Living in the multiverse (2005), hep-th/0511037

  77. Tegmark, M., Rees, M.J.: Why is the CMB fluctuation level 10−5? Astrophys. J. 499, 526 (1998), astro-ph/9709058

    Google Scholar 

  78. Banks, T., Dine, M., Gorbatov, E.: Is there a string theory landscape? JHEP 08, 058 (2004), hep-th/0309170

  79. Bousso, R., Harnik, R., Kribs, G.D., Perez, G.: Predicting the cosmological constant from the causal entropic principle. Phys. Rev. D 76, 043513 (2007), hep-th/0702115

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA, 94720-7300, USA

    Raphael Bousso

  2. Lawrence Berkeley National Laboratory, Berkeley, CA, 94720-8162, USA

    Raphael Bousso

Authors
  1. Raphael Bousso
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raphael Bousso.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bousso, R. The cosmological constant. Gen Relativ Gravit 40, 607–637 (2008). https://doi.org/10.1007/s10714-007-0557-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-007-0557-5

Keywords

Search

Navigation