Dynamics of scalar fields in an expanding/contracting cosmos at finite temperature

Abstract

This paper extends the study of the quantum dissipative effects of a cosmological scalar field by taking into account the cosmic expansion and contraction. Cheung, Drewes, Kang and Kim calculated the effective action and quantum dissipative effects of a cosmological scalar field. The analytic expressions for the effective potential and damping coefficient were presented using a simple scalar model with quartic interaction. Their work was done using Minkowski-space propagators in loop diagrams. In this work we incorporate the Hubble expansion and contraction of the comic background, and focus on the thermal dynamics of a scalar field in a regime where the effective potential changes slowly. We let the Hubble parameter, $H$, attain a small but non-zero value and carry out calculations to first order in $H$. If we set $H=0$ all results match those obtained previously in flat spacetime [1]. Interestingly we have to integrate over the resonances, which in turn leads to an amplification of the effects of a non-zero $H$. This is an intriguing phenomenon which cannot be uncovered in flat spacetime. The implications on particle creations in the early universe will be studied in a forthcoming work.

31 pages; 4 appendices. An appendix is added in Version 2 to calculate the free spectral function of a scalar field in de Sitter space, to justify the replacements proposed in (2.3)&(2.4) in order to rewrite the propagators obtained by Drewes, Mendizabal and Weniger in terms of cosmic time