  Motivated by the study of quantum fields in a Friedman-Robertson-Walker (FRW)
spacetime, the one-loop effective action for a scalar field defined in the
ultrastatic manifold $R\times H^3/\Gamma$, $H^3/\Gamma$ being the finite
volume, non-compact, hyperbolic spatial section, is investigated by a
generalisation of zeta-function regularisation. It is shown that additional
divergences may appear at one-loop level. The one-loop renormalisability of the
model is discussed and making use of a generalisation of zeta-function
regularisation, the one-loop renormalisation group equations are derived.
