Short distance physics and the consistency relation for scalar and tensor fluctuations in the inflationary universe

Physical Review D

Volumn 65, Issue 10, 2002, Pages

  Hui, Lam ^a   Kinney, William H ^a  

^a Department of Earth and Environmental Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; COSMOS; MODULATION; PHYSICS; SPECTROSCOPY; VACUUM;

EID: 0037053130     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.65.103507     Document Type: Article

References (44)

1. A.H. Guth, Phys. Rev. D 23, 347 (1981);
2. A.D. Linde, Phys. Lett. 108B, 389 (1982);
3. A. Albrecht and P.J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982).
4. W. Press, Phys. Scr. 21, 702 (1980);
5. V. Lukash, Pis'ma Zh. Eksp. Teor. Fiz. 31, 631 (1980);
6. V. Mukhanov and G. Chibisov, JETP Lett. 33, 532 (1981);
7. A. Starobinsky, Phys. Lett. 117B, 175 (1982);
8. S.W. Hawking, Phys. Lett. ibid. 115B, 295 (1982);
9. A.H. Guth and S.Y. Pi, Phys. Rev. Lett. 49, 1110 (1982);
10. J.M. Bardeen, P.J. Steinhardt, and M.S. Turner, Phys. Rev. D 28, 679 (1983);
11. L.F. Abbott and M.B. Wise, Nucl. Phys. B244, 541 (1984).
12. J. Martin and R.H. Brandenberger, Phys. Rev. D 63, 123501 (2001);
13. R.H. Brandenberger and J. Martin, Mod. Phys. Lett. A 16, 999 (2001);
14. J.C. Niemeyer, Phys. Rev. D 63, 123502 (2001);
15. J.C. Niemeyer and R. Parentani, Phys. Rev. D ibid. 64, 101301(R) (2001);
16. A. Kempf, Phys. Rev. D ibid. 63, 083514 (2001);
17. A. Kempf and J.C. Niemeyer, Phys. Rev. D ibid. 64, 103501 (2001).
18. Most authors so far explore the effect of modifying short-distance physics on scalar fluctuations by examining quantum fluctuations of a massless scalar field. The equation of motion obtained is actually closer to that for tensor modes than for scalar modes.
19. A.A. Starobinsky, Sov. Astron. Lett. 11, 133 (1985);
20. E.D. Stewart and D.H. Lyth, Phys. Lett. B 302, 171 (1993).
21. M. Kamionkowski, A. Kosowsky, and A. Stebbins, Phys. Rev. Lett. 78, 2058 (1997);
22. U. Seljak and M. Zaldarriaga, Phys. Rev. Lett. ibid. 78, 2054 (1997).
23. T. Tanaka, astro-ph/0012431;
24. A.A. Starobinsky, Pis'ma Zh. Eksp. Teor. Fiz. 73, 415 (2001).
25. G.W. Gibbons and S.W. Hawking, Phys. Rev. D 15, 2738 (1977);
26. T.S. Bunch and P.C.W. Davies, Proc. R. Soc. London A360, 117 (1978).
27. J.E. Lidsey, A.R. Liddle, E.W. Kolb, E.J. Copeland, T. Barreiro, and M. Abney, Rev. Mod. Phys. 69, 373 (1997).
28. See also J.C. Hwang, Phys. Rev. D 48, 3544 (1993)
29. and Class. Quantum Grav. 15, 1401 (1998), who derived similar expressions to ours for power spectra under a general vacuum. For the scalar mode, we focus here on the gauge invariant curvature fluctuation, which reduces to the inflaton fluctuation under the uniform curvature gauge adopted by the above reference.
30. L.P. Grishchuk, Sov. Phys. JETP 40, 409 (1974);
31. V.F. Mukhanov, Phys. Lett. B 218, 17 (1989).
32. N. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982);
33. see also J. Lesgourgues, D. Polarski, and A.A. Starobinsky, Nucl. Phys. B497, 479 (1997).
34. R. Easther, B. Greene, W.H. Kinney, and G. Shiu, Phys. Rev. D 64, 103502 (2001).
35. J.M. Bardeen, Phys. Rev. D 22, 1882 (1980).
36. 3 in the notation of [9]. Our choice of factors of 2π conforms to usual practice in large scale structure studies.
37. 3 in the notation of [9].
38. A.R. Liddle and D.H. Lyth, Phys. Rep. 231, 1 (1993). Note that η here follows the definition in this paper rather than [9].
39. S;
40. see also G. Shiu and S.-H.H. Tye, Phys. Lett. B 516, 421 (2001).
41. Starobinsky [7] argued that applying the same argument today gives a much stronger constraint. See [13] however for exceptions.
42. D. Polarski and A.A. Starobinsky, Phys. Lett. B 356, 196 (1995);
43. J. García-Bellido and D. Wands, Phys. Rev. D 52, 6739 (1995);
44. M. Sasaki and E.D. Stewart, Prog. Theor. Phys. 95, 71 (1996).