Skip to main content
Log in

Conditions for spontaneous homogenization of the Universe

  • Essay Awarded by the Gravity Research Foundation
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

The present-day Universe appears to be homogeneous on very large scales. Yet when the casual structure of the early Universe is considered, it becomes apparent that the early Universe must have been highly inhomogeneous. The current paradigm attempts to answer this problem by postulating the inflation mechanism However, inflation in order to start requires a homogeneous patch of at least the horizon size. This paper examines if dynamical processes of the early Universe could lead to homogenization. In the past similar studies seem to imply that the set of initial conditions that leads to homogenization is of measure zero. This essay proves contrary: a set of initial conditions for spontaneous homogenization of cosmological models can form a set of non-zero measure.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ehlers J., Geren P., Sachs R.K.: J. Math. Phys. 9, 1344 (1968)

    Article  ADS  Google Scholar 

  2. Stoeger W.R., Maarteens R., Ellis G.F.R.: Astrophys. J. 443, 1 (1955)

    Article  ADS  Google Scholar 

  3. Rees M.J., Sciama D.W.: Nature 217, 511 (1968)

    Article  ADS  Google Scholar 

  4. Inoue K.T., Silk J.: Astrophys. J. 648, 23 (2006)

    Article  ADS  Google Scholar 

  5. Inoue K.T., Silk J.: Astrophys. J. 664, 650 (2007)

    Article  ADS  Google Scholar 

  6. Riess A.G. et al.: Astrophys. J. 116, 1009 (1998)

    Google Scholar 

  7. Perlmutter S. et al.: Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  8. Eisenstein D.J. et al.: Astrophys. J. 633, 560 (2005)

    Article  ADS  Google Scholar 

  9. Hinshaw G. et al.: Astrophys. J. Suppl. 170, 288 (2007)

    Article  ADS  Google Scholar 

  10. Wald R.M.: General Relativity. The University of Chicago Press, Chicago (1984)

    MATH  Google Scholar 

  11. Ellis G.F.R.: Philosophy of physics. In: Butterfield, J., Earman, J., Gabby, D.M., Rhagard, P., Woods, J. (eds) Philosophy of Physics, pp. 11–12. Elsevier, Amsterdam (2006)

    Google Scholar 

  12. Linde A.D.: Inflation and Quantum Cosmology. Academic Press, Boston (1990)

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  14. Linde A.: Lect. Notes Phys. 738, 1 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  15. Goldwirth D.S., Piran T.: Phys. Rev. D 40, 3263 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  16. Goldwirth D.S., Piran T.: Phys. Rev. Lett. 64, 2852 (1990)

    Article  ADS  Google Scholar 

  17. Goldwirth D.S., Piran T.: Phys. Rept. 214, 223 (1992)

    Article  ADS  Google Scholar 

  18. Calzetta E., Sakellariadou M.: Phys. Rev. D 45, 2802 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  19. Misner C.W.: Astrophys. J. 151, 431 (1968)

    Article  ADS  Google Scholar 

  20. Hawking S.W., Ellis G.F.R.: The large scale structure of space-time. Cambridge University Press, Cambridge (1973)

    Book  MATH  Google Scholar 

  21. Ellis, G.F.R.: In: Sachs, R.K. (ed.) Proceedings of the XLVII Enrico Fermi Summer School, p. 105. Academic Press, New York, (1971); reprinted with historical comments in Gen. Rel. Grav. 41, 581 (2009).

  22. Collins C.B., Hawking S.W.: Astrophys. J. 180, 317 (1973)

    Article  MathSciNet  ADS  Google Scholar 

  23. Bonnor W.B.: Mon. Not. Roy. Astr. Soc. 167, 55 (1974)

    ADS  Google Scholar 

  24. Bonnor W.B., Tomimura N.: Mon. Not. Roy. Astr. Soc. 175, 85 (1976)

    ADS  Google Scholar 

  25. Silk J.: Astron. Astrophys. 59, 53 (1977)

    ADS  Google Scholar 

  26. Plebański J., Krasiński A.: An Introduction to General Relativity and Cosmology. Cambridge University Press, Cambridge (2006)

    Book  MATH  Google Scholar 

  27. van Elst H., Ellis G.F.R.: Class. Quant. Grav. 13, 1099 (1996)

    Article  MATH  ADS  Google Scholar 

  28. Lemaître G.: Ann. Soc. Sci. Bruxelles A 53, 51 (1933); English translation with historical comments in Gen. Relativ. Gravit. 29, 637 (1997)

    Google Scholar 

  29. Tolman, R.C.: Proc. Nat. Acad. Sci. USA 20, 169 (1934); reprinted with historical comments in Gen. Rel. Gravit. 29, 935 (1997)

    Google Scholar 

  30. Szekeres P.: Commun. Math. Phys. 41, 55 (1975)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. Roy S.R., Singh J.P.: Indian J. Pure Appl. Math. 13, 1285 (1982)

    MathSciNet  ADS  Google Scholar 

  32. Krasiński A.: Inhomogeneous Cosmological Models. Cambridge University Press, Cambridge (1977)

    Google Scholar 

  33. Coley A.A., McManus D.J.: Class. Quant. Grav. 11, 1261 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. McManus D.J., Coley A.A.: Class. Quant. Grav. 11, 2045 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  35. Bolejko K., Lasky P.D.: Mon. Not. R. Astron. Soc. 391, L59 (2008)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Krzysztof Bolejko.

Additional information

Fifth Award in the 2010 Essay Competition of the Gravity Research Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bolejko, K., Stoeger, W.R. Conditions for spontaneous homogenization of the Universe. Gen Relativ Gravit 42, 2349–2356 (2010). https://doi.org/10.1007/s10714-010-1020-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-010-1020-6

Keywords

Navigation