  For a Friedman-Robertson-Walker space-time in which the only contribution to
the stress-energy tensor comes from the renormalised zero-point energy (i.e.
the Casimir energy) of the fundamental fields the evolution of the universe
(the scale factor) depends upon whether the universe is open, flat or closed
and upon which fundamental fields inhabit the space-time. We calculate this
"Casimir effect" using the heat kernel method, and the calculation is thus
non-perturbative. We treat fields of spin $0,1/2,1$ coupled to the
gravitational background only. The heat kernels and/or zeta-functions for the
various spins are related to that of a non-minimally coupled one. A WKB
approximation is used in obtaining the radial part of that heat kernel. The
simulations of the resulting equations of motion seem to exclude the
possibility of a closed universe, $K=+1$, as these turn out to have an
overwhelming tendency towards a fast collapse - the details such as the rate of
this collapse depends on the structure of the underlying quantum degrees of
freedom: a non-minimal coupling to curvature accelerates the process. Only
$K=-1$ and K=0 will in general lead to macroscopic universes, and of these
$K=-1$ seems to be more favourable. The possibility of the scale factor being a
concave rather than a convex function potentially indicates that the problem of
the large Hubble constant is non-existent as the age of the universe need not
be less than or equal to the Hubble time. Note should be given to the fact,
however, that we are not able to pursue the numerical study to really large
times neither do simulations for a full standard model.
