A description of the transition from the inflationary epoch to radiation
domination requires the understanding of quantum fields out of thermal
equilibrium, particle creation and thermalisation. This can be studied from
first principles by solving a set of truncated real-time Schwinger-Dyson
equations, written in terms of the mean field (inflaton) and the field
propagators, derived from the two-particle irreducible effective action. We
investigate some aspects of this problem by considering the dynamics of a
slow-rolling mean field coupled to a second quantum field, using a \phi^2\chi^2
interaction. We focus on thermal effects. It is found that interactions lead to
an earlier end of slow-roll and that the evolution afterwards depends on
details of the heatbath.Comment: 25 pages, 11 eps figures. v2: paper reorganized, title changed,
conclusions unchanged, to appear in PR