  If the metric is chosen to depend exponentially on the conformal factor, and
if one works in a gauge where the conformal factor has the wrong sign
propagator, perturbative quantum gravity corrections can be partially resummed
into a series of terms each of which is ultraviolet finite. These new terms
however are not perturbative in some small parameter, and are not individually
BRST invariant, or background diffeomorphism invariant. With appropriate
parametrisation, the finiteness property holds true also for a full
phenomenologically relevant theory of quantum gravity coupled to (beyond the
standard model) matter fields, provided massive tadpole corrections are set to
zero by a trivial renormalisation.
