Advertisement

Stochastic de sitter (inflationary) stage in the early universe

  • A. A. Starobinsky
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 246)

Abstract

The dynamics of a large-scale quasi-homogeneous scalar field producing the de Sitter (inflationary) stage in the early universe is strongly affected by small-scale quantum fluctuations of the same scalar field and, in this way, becomes stochastic. The evolution of the corresponding large-scale space-time metric follows that of the scalar field and is stochastic also. The Fokker-Planck equation for the evolution of the large-scale scalar field is obtained and solved for an arbitrary scalar field potential. The average duration of the de-Sitter stage in the new inflationary scenario is calculated (only partial results on this problem were known earlier). Applications of the developed formalism to the chaotic inflationary scenario and to quantum inflation are considered. In these cases, the main unsolved problem lies in initial pre-inflationary conditions.

Keywords

Scalar Field Quantum Cosmology Stochastic Force Inflationary Scenario Effective Cosmological Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.A. Starobinsky, Phys.Lett. 91B (1980) 99.Google Scholar
  2. 2.
    A.H. Guth, Phys.Rev. D23 (1981) 347.Google Scholar
  3. 3.
    A.D. Linde, Pys.Lett. 108B (1982) 389.Google Scholar
  4. 4.
    A. Albrecht, P.J. Steinhardt, Phys.Rev.Lett. 48 (1982) 1220.Google Scholar
  5. 5.
    A.D. Linde, Pisma v ZhETF 38 (1983) 149; Phys.Lett. 129B (1983) 177.Google Scholar
  6. 6.
    L.A. Kofman, A.D. Linde, A.A. Starobinsky, Phys.Lett. 157B (1985) 361.Google Scholar
  7. 7.
    V.F. Mukhanov, G.V. Chibisov, Pisma v ZhETF 33 (1981) 549.Google Scholar
  8. 8.
    S.W. Hawking, I.G. Moss, Phys.Lett. 110B (1982) 35.Google Scholar
  9. 9.
    A.D. Linde, Phys. Lett. 116B (1982) 335.Google Scholar
  10. 10.
    A.A. Starobinsky, Phys.Lett. 117B (1982) 175.Google Scholar
  11. 11.
    J. Ellis, D.V. Nanopoulos, K.A. Olive, K.Tamvakis, Phys.Lett. 120B (1983) 331.Google Scholar
  12. 12.
    G.F. Mazenko, W.G. Unruh, R.M. Wald, Phys.Rev. D31 (1985) 273.Google Scholar
  13. 13.
    M. Evans, J.G. Mc Carthy, Phys.Rev. D31 (1985) 1799.Google Scholar
  14. 14.
    A. Vilenkin, Phys.Lett. 1158 (1982) 91.Google Scholar
  15. 15.
    A. Vilenkin, L.H. ford, Phys.Rev. D26 (1982) 1231.Google Scholar
  16. 16.
    A. Starobinsky, in: Proc. 6th Sov.Gravit.conf., Moscow 3–5 july 1984 (MGPI Press, Moscow, 1984), vol. 2, p. 39.Google Scholar
  17. 17.
    A. Starobinsky, in: Fundamental Interactions, ed. V.N. Ponomarev (MGPI Press, Moscow, 1984) p. 54.Google Scholar
  18. 18.
    S.W. Hawking, Phys.Lett. 115B (1982) 295.Google Scholar
  19. 19.
    A.H. Guth, S.-Y. Pi, Phys.Rev.Lett. 49 (1982) 1110.Google Scholar
  20. 20.
    J. Bardeen, P.I. Steinhardt, M.S. Turner, Phys.Rev. D28 (1983) 679.Google Scholar
  21. 21.
    A.A. Starobinsky, Pis'ma Astron.Zh. 9 (1983) 579 |Sov.Astron.Lett. 9 (1983) 3021.Google Scholar
  22. 22.
    L. Parker, S.A. Fulling, Phys.Rev. D7 (1973) 2357.Google Scholar
  23. 23.
    A.A. Starobinsky. Pis'ma As tron.Zh. 4 (1978) 1551 | Sov. Astron.Lett 4(1978) 821.Google Scholar
  24. 24.
    S.W. Hawking, Nucl.Phys. B239 (1984) 257.Google Scholar
  25. 25.
    D.N. Page, Class.Quantum Grav. 1 (1984) 417.Google Scholar
  26. 26.
    V.A. Belinsky, L.P. Grishchuk, I.M. Khalatnikov, Ya.B. Zeldovich, Phys.Lett. 155B (1985) 232.Google Scholar
  27. 27.
    J.B. Hartle, S.W. Hawking, Phys.Rev. D28 (1983) 2960.Google Scholar
  28. 28.
    Ya.B. Zeldovich, A.A. Starobinsky, Pis'ma Astron.Zh. 10 (1984) 323 | Sov.Astron. Lett. 10 (1984) 1351.Google Scholar
  29. 29.
    A.D. Linde, Zh.Eksp.Teor.Fiz. 87 (1984) 369; Lett. Nuovo Cimento 39 (1984) 401.Google Scholar
  30. 30.
    A. Vilenkin, Phys.Rev. D30 (1984) 509.Google Scholar
  31. 31.
    V.A. Rubakov, Pis'ma ZhETF, 39 (1984) 89; Phys.Lett. 148 (1984) 280.Google Scholar
  32. 32.
    E.P. Tryon, Nature 246 (1973) 396.Google Scholar
  33. 33.
    P.I. Fomin, Dokl.Akad.Nauk Ukrain. SSR (1975) 831.Google Scholar
  34. 34.
    L.P. Grishchuk, Ya.B. Zeldovich, in: Quantum structure of space-time, eds. M. Duff and C. Isham (Cambridge U.P., Cambridge, 1982) p. 409.Google Scholar
  35. 35.
    A. Vilenkin, Phys.Lett. 117B (1982) 25; Phys.Rev. D27 (1983) 2848.Google Scholar
  36. 36.
    A.A. Starobinsky, talk at the seminar in the P.K. Sternberg State Astronomical Institute (Moscow, November 1983), unpublished.Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • A. A. Starobinsky
    • 1
    • 2
  1. 1.Landau Institute for Theoretical PhysicsMoscowU.S.S.R.
  2. 2.ER 176 C.N.R.S. “Département d'Astrophysique Fondamentale”Observatoire de MeudonMeudon Principal CedexFrance

Personalised recommendations