  The treatment of a quantized field in a curved spacetime requires the study
of backreaction of the field on the spacetime via the semiclassical Einstein
equation. We consider a free scalar field in spatially flat Robertson-Walker
space time. We require the state of the field to allow for a renormalized
semiclassical stress tensor. We calculate the sigularities of the stress tensor
restricted to equal times in agreement with the usual renormalization
prescription for Hadamard states to perform an explicit renormalization. The
dynamical system for the Robertson Walker scale parameter $a(t)$ coupled to the
scalar field is finally derived for the case of conformal and also general
coupling.
