DSF preprint 95/6, revised version QUANTUM EFFECTS IN FRIEDMANN-ROBERTSON-WALKER COSMOLOGIES

Electrodynamics for self-interacting scalar elds in spatially at FriedmannRobertson-Walker space-times is studied. The corresponding one-loop eld equation for the expectation value of the complex scalar eld in the conformal vacuum is derived. For exponentially expanding universes, the equations for the Bogoliubov coe cients describing the coupling of the scalar eld to gravity are solved numerically. They yield a non-local correction to the Coleman-Weinberg e ective potential which does not modify the pattern of minima found in static de Sitter space. Such a correction contains a dissipative term which, accounting for the decay of the classical con guration in scalar eld quanta, may be relevant for the reheating stage. The physical meaning of the non-local term in the semiclassical eld equation is investigated by evaluating this contribution for various background eld con gurations. PACS numbers: 0260, 0370, 0420, 1115, 9880