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 [78, 77, 79, 80]. This is not necessarily inconsistent with having neglected action terms of higher order in when considering semiclassical gravity as an effective theory . It is, in fact, consistent with the closed connection of stochastic gravity with the large expansion of quantum gravity interacting with matter fields.
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