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We study the non-equilibrium dynamics of a system of coupled scalar fields ina Friedmann-Robertson-Walker (FRW) universe. We consider the evolution ofspatially homogeneous "classical" fields and of their quantum fluctuationsincluding the quantum backreaction in the one-loop approximation. We discuss inparticular the dimensional regularisation of the coupled system and a specialsubtraction procedure in order to obtain the renormalised equations of motionand the renormalised energy-momentum tensor and ensure that the energy iswell-defined and covariantly conserved. These results represent at the sametime a theoretical analysis and a viable scheme for stable numericalsimulations. As an example for an application of the general formalism, wepresent simulations for a hybrid inflationary model.

Coupled scalar fields in a flat FRW universe: renormalisation