Density parameter and the anthropic principle

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 60, Issue 2, 1999, Pages

  Vilenkin, Alexander ^c  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b OSAKA UNIVERSITY   (Japan)

^c TUFTS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 16444381514     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.60.023501     Document Type: Article

References (67)

1. B. Carter, in I.A.U. Symposium, edited by M. S. Longair (Reidel, Dordrecht, 1974), Vol. 63
2. B. B. Carr and M. J. Rees, Nature (London) 278, 605 (1979)
3. J. Barrow and F. Tipler, The Anthropic Cosmological Principle (Clarendon, Oxford, England, 1986)
4. S. Weinberg, Phys. Rev. Lett. 59, 2607 (1987)
5. A. D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Chur, Switzerland, 1990)
6. J. Garcia-Bellido and A. Linde, Phys. Rev. D 51, 429 (1995).
7. A. Vilenkin, Phys. Rev. Lett. 74, 846 (1995).
8. A very similar approach was used by Carter 4, Leslie 5 and Gott 6 to estimate the expected lifetime of our species. Gott also applied it to estimate the lifetimes of various political and economic structures, including the journal “Nature” where his article was published.
9. B. Carter (unpublished).
10. J. Leslie, Mind 101, 521 (1992).
11. J. R. Gott III, Nature (London) 363, 315 (1993).
12. J. R. Gott, Nature (London) 295, 304 (1982)
13. J. R. Gott and T. S. Stalter, Phys. Lett. 136B, 157 (1984)
14. A. Guth and E. Weinberg, Nucl. Phys. B212, 321 (1983)
15. M. Sasaki, T. Tanaka, K. Yamamoto, and J. Yokoyama, Phys. Lett. B 317, 510 (1993)
16. K. Yamamoto, M. Sasaki, and T. Tanka, Astrophys. J. 455, 412 (1995)
17. M. Bucher, A. Goldhaber, and N. Turok, Phys. Rev. D 52, 5538 (1995)
18. Phys. Rev. DA. M. Green and A. R. Liddle, 55, 609 (1997)
19. Phys. Rev. DJ. Garcia-Bellido and A. Linde, 55, 7480 (1997).
20. M. Bucher, A. S. Goldhaber, and N. Turok, Phys. Rev. D 52, 3314 (1995).
21. A. D. Linde, Phys. Lett. B 351, 99 (1995)
22. A. D. Linde and A. Mezhlumian, Phys. Rev. D 52, 6789 (1995).
23. J. Garcia-Bellido, J. Garriga, and X. Montes, Phys. Rev. D 57, 4669 (1998).
24. A. Vilenkin and S. Winitzki, Phys. Rev. D 55, 548 (1997).
25. A. Linde, D. Linde, and A. Mezhlumian, Phys. Rev. D 49, 1783 (1994)
26. Phys. Rev. DA. Linde and A. Mezhlumian, 53, 4267 (1996).
27. A. Vilenkin, Phys. Rev. D 52, 3365 (1995).
28. J. Garcia-Bellido and A.D. Linde, Phys. Rev. D 51, 429 (1995).
29. S. Parke, Phys. Lett. 121B, 313 (1983).
30. S. Coleman, Phys. Rev. D 15, 2929 (1977)
31. Phys. Rev. DS. Coleman and F. De Luccia, 21, 3305 (1980).
32. G. Efstathiou, Mon. Not. R. Astron. Soc. 274, L73 (1995).
33. A. Vilenkin, in Cosmological Constant and Evolution of the Universe, edited by K. Sato, T. Suginohara, and N. Sugiyama (Universal Academy Press, Tokyo, 1996).
34. S. Weinberg, in Critical Dialogues in Cosmology, edited by N. Turok (World Scientific, Singapore, 1997).
35. H. Martel, P. R. Shapiro, and S. Weinberg, Astrophys. J. 492, 29 (1998).
36. W. H. Press and P. Schechter, Astrophys. J. 187, 425 (1974).
37. A. R. Liddle, D. H. Lyth, D. Roberts, and P. P. T. Viana, Mon. Not. R. Astron. Soc. 278, 644 (1996).
38. P. J. E. Peebles, The Large Scale Structure of the Universe (Princeton University Press, Princeton, NJ, 1980).
39. P. B. Lilje, Astrophys. J. Lett. 386, L33 (1992)
40. S. Colafrancesco and N. Vittorio, Astrophys. J. 422, 443 (1994).
41. C. Lacey and S. Cole, Mon. Not. R. Astron. Soc. 262, 627 (1993).
42. A careful treatment of the variation of (Formula presented) in the case of a flat universe with a cosmological constant has been given by Martel, Shapiro and Weinberg (MSW) who calculated the fraction of clustered matter (Formula presented) to find an anthropic probability distribution for (Formula presented) 20. They considered density fluctuations having the form of a spherical overdense region surrounded by a compensating spherical underdense shell, with a fixed ratio s of overdense to underdense volumes, and calculated (Formula presented) using the exact collapse criterion for such fluctuations. MSW emphasize that their results are insensitive to the choice of s. Now, we note that for large s, the formula they obtained for (Formula presented) their Eq. (26), reduces to the Press-Schechter formula (23) that we use here, with (Formula presented). This indicates that Press-Schechter formalism would be an adequate approximation in MSW problem as well.
43. P. J. E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, NJ, 1993).
44. M. Tegmark and M. Rees, Astrophys. J. 499, 526 (1998).
45. M. J. Rees and J. P. Ostriker, Mon. Not. R. Astron. Soc. 179, 541 (1977)
46. J. Silk, Astrophys. J. 211, 638 (1977).
47. M. Sasaki and T. Tanaka, Phys. Rev. D 54, R4705 (1996)
48. Phys. Rev. DK. Yamamoto, M. Sasaki, and T. Tanaka, 54, 5031 (1996)
49. Phys. Rev. DM. Sasaki, T. Tanaka, and Y. Yakushige, 56, 616 (1997).
50. J. Garriga, X. Montes, M. Sasaki, and T. Tanaka, Nucl. Phys. B513, 343 (1998).
51. J. Garcia-Bellido, Phys. Rev. D 54, 2473 (1996)
52. Phys. Rev. DJ. Garcia-Bellido56, 3225 (1997)
53. J. Garcia-Bellido“Single Bubble Open Inflation: An Overview,” CERN report, hep-ph/9803270.
54. J. Garriga, Phys. Rev. D 54, 4764 (1996).
55. R. H. Dicke, Nature (London) 192, 440 (1962).
56. A. Vilenkin, talk given at the first RESCEU Symposium, Tokyo (1995).
57. J. Silk (private communication).
58. S. W. Hawking and N. Turok, Phys. Lett. B 425, 25 (1998).
59. A. D. Linde, Phys. Rev. D 58, 083514 (1998)
60. W. Unruh, U.B.C. report, gr-qc/9803050
61. R. Bousso and A. Linde, Phys. Rev. D 58, 083503 (1998)
62. Z. C. Wu, Gen. Relativ. Gravit. 30, 1639 (1998).
63. A. Vilenkin, Phys. Rev. D 57, 7069 (1998).
64. See, e.g., M. Davis, in Critical Dialogues in Cosmology, edited by N. Turok (World Scientific, Singapore, 1997), for evidence of homogeneity of large-scale galaxy distribution.
65. J. Garriga and V. F. Mukhanov, Phys. Rev. D 56, 2439 (1997).
66. J. M. Bardeen, J. R. Bond, N. Kaiser, and A. S. Szalay, Astrophys. J. 304, 15 (1986).
67. J. A. Peacock and S. J. Dodds, Mon. Not. R. Astron. Soc. 267, 1020 (1994).