  We analyze critically the renormalization of quantum fields in cosmological
spacetimes, using non covariant ultraviolet cutoffs. We compute explicitly the
counterterms necessary to renormalize the semiclassical Einstein equations,
using comoving and physical ultraviolet cutoffs. In the first case, the
divergences renormalize bare conserved fluids, while in the second case it is
necessary to break the covariance of the bare theory. We point out that, in
general, the renormalized equations differ from those obtained with covariant
methods, even after absorbing the infinities and choosing the renormalized
parameters to force the consistency of the renormalized theory. We repeat the
analysis for the evolution equation for the mean value of an interacting scalar
field
