- Access by Xinjiang University
Anisotropy dissipation in the early Universe: Finite-temperature effects reexamined
Phys. Rev. D 41, 1054 – Published 15 February, 1990
DOI: https://doi.org/10.1103/PhysRevD.41.1054
Abstract
We reexamine the role that finite-temperature effects play in the dissipation of the initial anisotropy of the Universe. The issue was previously studied both in the zero- and finite-temperature cases. Our results show that the finite-temperature corrections do not introduce new qualitative behavior and that the anisotropy dissipation scenario is approximately the same as in the zero-temperature case. We use a formalism that is based on the extension to finite temperature of the closed-time-path method (it can be used to study systems out of thermal equilibrium). The effective equations that we obtain are real and causal. We compare our results with others obtained in the zero- and finite-temperature cases. We discuss some qualitative differences between the formalisms that are more frequently used to study real-time processes at finite temperature.
References (28)
- R. M. Wald, General Relativity (The University of Chicago Press, Chicago, 1984)
- N. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982)
- J. Halliwell, Phys. Rev. D 39, 2912 (1989) T. Padmanabhan, ibid. 39, 2924 (1989)
- P. R. Anderson, Phys. Rev. D 28, 271 (1983) ibid.28, 2695 (1983) ibid.29, 615 (1984) ibid.33, 1567 (1986)
- Ya. B. Zel'dovich, Pis'ma Zh. Eksp. Teor. Fiz. 12, 443 (1970) [JETP Lett. 12, 307 (1970)]
- Ya. B. Zel'dovich and A. A. Starobinski, Zh. Eksp. Teor. Fiz. 61, 2161 (1971) [Sov. Phys.—JETP 34, 1159 (1972)]
- B. L. Hu and L. Parker, Phys. Rev. D 17, 933 (1978)
- J. B. Hartle and B. L. Hu, Phys. Rev. D 20, 1772 (1979) ibid.21, 2756 (1980)
- J. B. Hartle, Phys. Rev. D 22, 2091 (1980) ibid.23, 2121 (1981)
- E. Calzetta and B. L. Hu, Phys. Rev. D 35, 495 (1987)
- J. S. Schwinger, J. Math. Phys. 2, 407 (1961) L. V. Keldish, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys.—JETP 20, 1018 (1965)] G. Zhou, Z. Su, B. Hao, and L. Yu, Phys. Rep. 118, 1 (1985)
- B. L. Hu, Physica A 158, 399 (1989)
- R. D. Jordan, Phys. Rev. D 36, 3604 (1986)
- P. Amsterdamski, Phys. Rev. D 35, 1209 (1987)
- H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, 1982)
- P. Amsterdamski, Phys. Rev. D 35, 2323 (1987) N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987)
- Y. Yamanaka, in Proceedings of the CAP NSERC Summer Institute in Theoretical Physics: Two Dimensional Field Theory, Edmonton, Canada, 1987, edited by F. C. Khanna, H. Umezawa, G. Kunstatter, and H. C. Lee (World Scientific, Singapore, 1988)
- A. J. Niemi and G. W. Semenoff, Ann. Phys. (N.Y.) 152, 105 (1981) Nucl. Phys. B230 [FS10], 181 (1984)
- B. L. Hu, Phys. Lett. 108B, 9 (1982) ibid.123B, 189 (1983)
- E. Calzetta and B. L. Hu, Phys. Rev. D 37, 2878 (1099)
- N. Weiss and G. Semenoff, Phys. Rev. D 31, 689 (1985)
- R. D. Jordan, Phys. Rev. D 33, 444 (1986)
- R. Jackiw, Phys. Rev. D 9, 1686 (1984)
- J. M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974)
- A. J. Niemi, Phys. Lett. B 203, 425 (1988)
- E. Calzetta and B. L. Hu, Phys. Rev. D 39, 380 (1989)
- J. P. Paz, University of Maryland report, 1989 (unpublished)
- B. L. Hu, J. P. Paz, and A. Stylianopoulos (in preparation)