For background solutions of semiclassical gravity
with other scales present apart from the Planck scales (for
instance, for matter fields in a thermal state), stress-energy
fluctuations may be important at larger scales. For such
backgrounds, stochastic semiclassical gravity might predict
correlation functions with characteristic correlation lengths
larger than the Planck scales. It seems quite plausible,
nevertheless, that these correlation functions would remain
non-analytic in their characteristic correlation lengths. This
would imply that these correlation functions could not be obtained
from a calculation involving a perturbative expansion in the
characteristic correlation lengths. In particular, if these
correlation lengths are proportional to the Planck constant , the gravitational correlation functions could not
be obtained from an expansion in
. Hence, stochastic
semiclassical gravity might predict a behavior for gravitational
correlation functions different from that of the analogous
functions in perturbative quantum gravity [79, 78, 77, 80]. This is not
necessarily inconsistent with having neglected action terms of
higher order in
when considering semiclassical gravity
as an effective theory [91]. It is, in fact,
consistent with the closed connection of stochastic gravity with
the large
expansion of quantum gravity
interacting with
matter fields.