- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Thermal equilibrium in de Sitter space

Ian H. Redmount

Fernando Ruiz Ruiz

  • Institute of Astronomy, University of Cambridge, The Observatories, Madingley Road, Cambridge, CB3 0HA, England

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 3 Silver Street, Cambridge, CB3 9EW, England

PDF

Phys. Rev. D 39, 2289 – Published 15 April, 1989

DOI: https://doi.org/10.1103/PhysRevD.39.2289

Abstract

Thermal-equilibrium quantum states are constructed for free scalar fields in (N+1)-dimensional de Sitter space. The states are described by density matrices of ‘‘thermal’’ form, satisfying the von Neumann equation associated with the appropriate functional Schrödinger equation. These solutions exist only for fields with mass and/or curvature coupling corresponding to conformal invariance. The temperature associated with such a state obeys the classical red-shift law. States exist with any temperature value at any given time; the zero-temperature limit is the Euclidean vacuum state. The total field energy of a thermal state above that of the Euclidean vacuum is finite and positive. This excitation energy consists of one contribution which red-shifts classically, but it can also contain a contribution which grows in time as the radius of the space.

View figure in article

References (33)

  1. J. S. Dowker and R. Critchley, Phys. Rev. D 15, 1484 (1977).
  2. G. W. Gibbons and M. J. Perry, Proc. R. Soc. London A358, 467 (1978).
  3. J. S. Dowker and G. Kennedy, J. Phys. A 11, 895 (1978).
  4. M. B. Altaie and J. S. Dowker, Phys. Rev. D 18, 3557 (1978).
  5. R. Critchley, P. C. W. Davies and G. Kennedy, Phys. Lett. 112B, 331 (1982).
  6. G. Kennedy, J. Phys. A 11, L77 (1978).
  7. B. L. Hu, Phys. Lett. 103B, 331 (1981).
  8. B. L. Hu, Phys. Lett. 108B, 19 (1982).
  9. I. T. Drummond, Nucl. Phys. B190, 93 (1981).
  10. B. L. Hu, in The Very Early Universe, edited by G. W. Gibbons, S. W. Hawking, and S. T. C. Siklos (Cambridge University Press, Cambridge, England, 1983), pp. 343–352.
  11. B. L. Hu, Phys. Lett. 123B, 189 (1983).
  12. G. Semenoff and N. Weiss, Phys. Rev. D 31, 689 (1985).
  13. L. F. Chen and B. L. Hu, Phys. Lett. 160B, 36 (1985).
  14. B. L. Hu, R. Critchley and A. Stylianopoulos, Phys. Rev. D 35, 510 (1987).
  15. O. E´boli, R. Jackiw and S.-Y. Pi, Phys. Rev. D 37, 3557 (1988).
  16. A. H. Guth, Phys. Rev. D 23, 347 (1981).
  17. K. Freese, C. T. Hill and M. Mueller, Nucl. Phys. B255, 693 (1985).
  18. B. Ratra, Phys. Rev. D 31, 1931 (1985).
  19. S. Wada, Phys. Rev. Lett. 59, 2375 (1987).
  20. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), frontispiece.
  21. M. Gutzwiller, Helv. Phys. Acta 29, 313 (1956).
  22. N. A. Chernikov and E. A. Tagirov, Ann. Inst. Henri Poincaré 9, 109 (1968).
  23. I. H. Redmount and S. Takagi, Phys. Rev. D 37, 1443 (1988).
  24. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982), pp. 87 and 88.
  25. J. Traschen and C. T. Hill, Phys. Rev. D 33, 3519 (1986).
  26. Higher Transcendental Functions (Bateman Manuscript Project), edited by A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (McGraw-Hill, New York, 1953), Vol. II, pp. 232–242.
  27. Birrell and Davies, Quantum Fields in Curved Space (Ref. 24), p. 44.
  28. H. E. Kandrup, Phys. Rev. D 37, 3505 (1988).
  29. R. P. Feynman, Statistical Mechanics (Benjamin, Reading, MA, 1972), p. 51.
  30. B. Allen, Phys. Rev. D 32, 3136 (1985).
  31. M. S. Turner and L. M. Widrow, Phys. Rev. D 37, 3428 (1988).
  32. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2738 (1977).
  33. A. Vilenkin and L. H. Ford, Phys. Rev. D 26, 1231 (1982).

Outline

Information

Phys. Rev. D 39, 2289– Published 15 April, 1989
  • Received 13 December 1988

© 1989 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation