Probability distribution for [Formula presented] in open-universe inflation

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 55, Issue 2, 1997, Pages 548-559

  Vilenkin, Alexander ^a   Winitzki, Serge ^a  

^a TUFTS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001417240     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.55.548     Document Type: Article

References (35)

1. For a review of inflation, see, e.g., A. D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Chur, Switzerland, 1990);
2. K. A. Olive, Phys. Rep.190, 307 (1990).
3. J. R. Gott III, Nature (London)295, 304 (1982);
4. J. R. Gott III and T. Statler, Phys. Lett.136B, 157 (1984).
5. M. Bucher, A. S. Goldhaber, and N. Turok, Phys. Rev. D52, 3314 (1995);
6. M. Bucher and N. Turok, 52, 5538 (1995).
7. T. Tanaka and M. Sasaki, Phys. Rev. D50, 6444 (1994);
8. K. Yamamoto, T. Tanaka, and M. Sasaki, Phys. Rev. D51, 2968 (1995).
9. A. D. Linde, Phys. Lett. B351, 99 (1995);
10. A. D. Linde and A. Mezhlumian, Phys. Rev. D52, 6789 (1995).
11. J. Garriga, Phys. Rev. D54, 4764 (1996);
12. J. Garcia-Bellido, 54, 2473 (1996).
13. A. Vilenkin, Phys. Rev. Lett.74, 846 (1995).
14. B. Carter, in I.A.U. Symposium, Vol. 63, edited by M. S. Longair (Reidel, Dordrecht, 1974).
15. B. J. Carr and M. J. Rees, Nature (London)278, 605 (1979).
16. J. Barrow and F. Tipler, The Anthropic Cosmological Principle (Clarendon Press, Oxford, England, 1986).
17. A. D. Linde, Particle Physics and Inflationary Cosmology [1].
18. J. Leslie, Mind 101, 521 (1992).
19. The thermalization temperature is a convenient reference point, but of course this choice is arbitrary, and one can use any other reference temperature.
20. A. D. Linde, D. A. Linde, and A. Mezhlumian, Phys. Rev. D49, 1783 (1994).
21. J. Garcia-Bellido, A. D. Linde, and D. A. Linde, Phys. Rev. D50, 730 (1994).
22. A. Vilenkin, Phys. Rev. D52, 3365 (1995).
23. S. Winitzki and A. Vilenkin, Phys. Rev. D53, 4298 (1996).
24. For a recent review of this stochastic approach to inflation, see 14.
25. The function (Formula presented) is rather complicated: (Formula presented)Its explicit form will not be useful for us, and we can use the linear fit (31) to visualize its behavior.
26. F. C. Adams, Phys. Rev. D48, 2800 (1993).
27. The spectrum of density fluctuations is also (Formula presented) dependent, but this dependence is negligible on scales small compared to the curvature radius of the bubble. This range of scales includes the galactic scale, except for very small values of (Formula presented). Since (Formula presented) drops exponentially fast as (Formula presented) is decreased, we expect that our conclusions will not be substantially modified by taking into account the (Formula presented)-dependence of the fluctuation spectrum.
28. It should be emphasized that our evaluation of (Formula presented) can serve only as a very rough estimate. In particular, for very low values of (Formula presented), galaxies are formed at a high redshift (Formula presented), and their properties may be very different from those observed in our part of the universe. For example, a higher gas density in the galaxy can affect the rate of star formation, and thus the number of inhabitable stellar systems.
29. G. Steigman and J. E. Felten, Space Sci. Rev.74, 245 (1995); SPSRA4A. D. Linde and A. Mezhlumian, in Ref. 5.
30. S. Weinberg, Phys. Rev. Lett.59, 2607 (1987).
31. G. Efstathiou, Mon. Not. R. Astron. Soc.274, L73 (1995).MNRAA4
32. A. Vilenkin, in Cosmological Constant and the Evolution of the Universe, edited by K. Sato, T. Suginohara, and N. Sugiyama (Universal Academy Press, Tokyo, 1996).
33. V. A. Berezin, V. A. Kuzmin, and I. I. Tkachev, Phys. Lett.120B, 91 (1983);
34. Phys. Rev. D36, 2919 (1987); also in Quantum Gravity, edited by by M. A. Markov, V. A. Berezin, and V. P. Frolov (World Scientific, Singapore, 1985), p. 781;
35. R. BasuA. H. Guth, and A. Vilenkin, Phys. Rev. D44, 340 (1991).