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

This study extends the investigation of quantum dissipative effects of a cosmological scalar field by taking into account cosmic expansion and contraction. Cheung, Drewes, Kang, and Kim calculated the effective action and quantum dissipative effects of a cosmological scalar field in a recent work, where analytical expressions for the effective potential and damping coefficient were presented using a simple scalar model with quartic interactions, and the work was conducted using Minkowski-space propagators in loop diagrams. In this work, we incorporate the Hubble expansion and contraction of the cosmic background and focus on the thermal dynamics of a scalar field in a regime where the effective potential changes slowly. Given that the Hubble parameter, H, attains a small but non-zero value, we carry out calculations to the first order in H. If we set H = 0, all results match those in flat spacetime. Interestingly, we must 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 study.