  The quantum contributions to the gravitational action are relatively easy to
calculate in the higher derivative sector of the theory. However, the
applications to the post-inflationary cosmology and astrophysics require the
corrections to the Einstein-Hilbert action and to the cosmological constant,
and those we can not derive yet in a consistent and safe way. At the same time,
if we assume that these quantum terms are covariant and that they have relevant
magnitude, their functional form can be defined up to a single free parameter,
which can be defined on the phenomenological basis. It turns out that the
quantum correction may lead, in principle, to surprisingly strong and
interesting effects in astrophysics and cosmology.
