Prog. Theor. Phys. Vol. 66 No. 2 (1981) pp. 498-507
On Quantum Theory of General-Relativistic Many-Particle Systems. II
— Friedman-Robertson-Walker Universes with Quantized Matter
Department of Physics, Tokyo Institute of Technology, Oh-okayama, Tokyo 152
(Received December 19, 1980)
A formalism of quantum many-particle systems in curved spacetime is discussed in a previous paper. In the present paper, as an application of our formalism, Friedman-Robertson-Walker universes filled with quantized matter and raditation field are considered. The `temperature' of the universe will decrease inverse proportionally to the linear magnitude of the expanding universe. It becomes clear that the stress tensor consists of two parts, one is a contribution form particles in thermal equilibrium and the other is from the quantum theoretical vacuum, and these are independent of each other. This implies that there occurs no particle production in the present case, as suggested by Parker. The expectation value of the stress tensor calculated in this way is the quantity which should appear in Einstein's equation when one considers the early stage of the universe.
DOI : 10.1143/PTP.66.498
- I. Ichinose, Prog. Theor. Phys. 65 (1981), 2023[PTP].
- S. Weinberg, Gravitation and Cosmology (John Wiley, New York, 1972), chap. 15.
- L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, 1962), chap. 12.
B. Mashhoon, Phys. Rev. D 8 (1973), 4297[APS].
L. H. Ford, Phys. Rev. D 11 (1975), 3370[APS].
M. B. Altaie and J. S. Dowker, Phys. Rev. D 18 (1978), 3557[APS].
- For proper-time formalism in the usual case, see
B. S. DeWitt, Phys. Rep. 19 (1975), 295[CrossRef].
- E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford, 1948).
- For trace anomaly in dimensional regularization, see
L. S. Brown, Phys. Rev. D 15 (1977), 1469[APS].
L. S. Brown and J. P. Cassidy, Phys. Rev. D 15 (1977), 2810[APS].
R. M. Wald, Ann. of Phys. 110 (1978), 472[CrossRef].
- L. Parker, in Recent Developments in Gravitation, Cargese, 1978, ed., M. Levy and S. Deser (Plenum, New York, 1979) and references cited therein.
P. C. W. Davies, S. A. Fulling, S. M. Christensen and T. S. Bunch, Ann. of Phys. 109 (1977), 108[CrossRef].
T. S. Bunch and P. C. W. Davies, Proc. Roy. Soc. A 357 (1977), 381.
P. C. W. Davies, Phys. Lett. B 68 (1977), 402[CrossRef].
M. V. Fischetti, J. B. Hartle and B. L. Hu, Phys. Rev. D 20 (1979), 1757[APS].