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 [1] 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 [1] in flat spacetime. 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.

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