  Effects of quantized free scalar fields in cosmological spacetimes with Big
Rip singularities are investigated. The energy densities for these fields are
computed at late times when the expansion is very rapid. For the massless
minimally coupled field it is shown that an attractor state exists in the sense
that, for a large class of states, the energy density of the field
asymptotically approaches the energy density it would have if it was in the
attractor state. Results of numerical computations of the energy density for
the massless minimally coupled field and for massive fields with minimal and
conformal coupling to the scalar curvature are presented. For the massive
fields the energy density is seen to always asymptotically approach that of the
corresponding massless field. The question of whether the energy densities of
quantized fields can be large enough for backreaction effects to remove the Big
Rip singularity is addressed.
