Violation of the weak energy condition in inflating spacetimes

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 56, Issue 2, 1997, Pages 717-723

  Borde, Arvind ^a   Vilenkin, Alexander ^a  

^a TUFTS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000324195     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.56.717     Document Type: Article

References (52)

1. For reviews of inflation see, for example, S. K. Blau and A. H. Guth, in 300 Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1987);
2. A. D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Chur, Switzerland, 1990);
3. E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, New York, 1990).
4. A. Vilenkin, Phys. Rev. D 27, 2848 (1983).
5. A. D. Linde, Phys. Lett. B 175, 395 (1986).
6. M. Aryal and A. Vilenkin, Phys. Lett. B 199, 351 (1987).
7. A. S. Goncharov, A. D. Linde, and V. F. Mukhanov, Int. J. Mod. Phys. A 2, 561 (1987).
8. K. Nakao, Y. Nambu, and M. Sasaki, Prog. Theor. Phys. 80, 1041 (1988).
9. A. Linde, D. Linde, and A. Mezhlumian, Phys. Rev. D 49, 1783 (1994).
10. The quantum fluctuations make (Formula presented) go up and down the potential. This means that different parts of the Universe thermalize at different times. Further, at any given time, there is a nonzero probability for some regions of the Universe to still be inflating.
11. In fact, the “horizon size” itself will be subject to fluctuations, but is a meaningful concept when averaged over this large scale.
12. See, for example, some of the discussions in The Very Early Universe, edited by G. W. Gibbons and S. W. Hawking (Cambridge University Press, Cambridge, England, 1983).
13. A. D. Linde, in The Very Early Universe 10.
14. P. J. Steinhardt, in The Very Early Universe 10.
15. A. Vilenkin, Phys. Rev. D 46, 2355 (1992).
16. A spacetime is past-geodesically complete if all timelike and null geodesics can be extended in the past direction to infinite values of their affine parameters.
17. A. Borde and A. Vilenkin, Phys. Rev. Lett. 72, 3305 (1994).
18. A. Borde and A. Vilenkin, in Relativistic Astrophysics: The Proceedings of the Eighth Yukawa Symposium, edited by M. Sasaki (Universal Academy Press, Japan, 1995).
19. A. Borde and A. Vilenkin, Int. J. Mod. Phys. (to be published).
20. A. Borde, report 1996 (unpublished).
21. A. Borde, Phys. Rev. D 50, 3392 (1994).
22. E. Farhi and A. H. Guth, Phys. Lett. B 183, 149 (1987).
23. E. Farhi, A. H. Guth, and J. Guven, Nucl. Phys. B339, 417 (1990).
24. L. Fischler, D. Morgan, and J. Polchinski, Phys. Rev. D 41, 2638 (1990).
25. A. Linde, Nucl. Phys. B372, 421 (1992).
26. F. J. Tipler, Phys. Rev. D 17, 2521 (1978).
27. G. Galloway, Manuscr. Math. 35, 209 (1981).MSMHB2
28. T. Roman, Phys. Rev. D 33, 3526 (1986);
29. 37, 546 (1988).
30. A. Borde, Class. Quantum Grav. 4, 343 (1987).
31. G. Veneziano, in String Gravity and Physics at the Planck Energy Scale, edited by N. Sanchez and A. Zichichi (Kluwer Academic, Dordrecht, 1996).
32. M. Gasperini, in String Gravity and Physics at the Planck Energy Scale 30.
33. There are violations of the weak energy condition in such cosmologies as pointed out by S. Kar, Report No., 1996(unpublished).
34. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Spacetime (Cambridge University Press, Cambridge, England, 1973).
35. É. Flanagan and R. M. Wald, Phys. Rev. D 54, 6233 (1996).
36. L. H. Ford, Proc. R. Soc. London A364, 227 (1978);
37. Phys. Rev. D 43, 3972 (1991).
38. L. H. Ford and T. A. Roman, Phys. Rev. D 41, 3662 (1990);
39. 44, 1328 (1992);
40. 51, 4277 (1995);
41. 53, 1988 (1996);
42. 53, 5496 (1996).
43. M. Pfenning and L. H. Ford Phys. Rev. D 55, 4813 (1997).
44. M. Pfenning and L. H. Ford (to be published).
45. A short discussion of this question also appears in Ref. 18.
46. J. R. Gott, Nature (London) 295, 304 (1982).
47. M. Bucher, A. S. Goldhaber, and N. Turok, Phys. Rev. D 52, 3314 (1995).
48. K. Yamamoto, M. Sasaki, and T. Tanaka, Astrophys. J. 455, 412 (1995).
49. A. D. Linde, Phys. Lett. B 351, 99 (1995).
50. S. Kar, Phys. Rev. D 49, 862 (1994).
51. S. Kar and D. Sahdev, Phys. Rev. D 53, 722 (1996).
52. T. Fukuyama, M. Hatakeyama, M. Miyoshi, M. Morikawa, and A. Nakamichi, Report No., 1996 (unpublished).