The Schwinger-Keldysh technique in a cosmological context

In the problems of quantum cosmology, a situation arises when the partition function of the effective theory is given by a functional integral with a Keldysh contour supplemented by a Euclidean functional integral specifying the initial state. For such theories, the construction of a perturbation theory on an arbitrary homogeneous background is technically non-trivial and requires the development of some special formalism. I will tell you how to develop such a formalism, as well as some interesting particular examples. In particular, it turns out that if the Euclidean action obeys some specific real condition, the expressions for the Green's functions have the form of ordinary thermal Green's functions with a special type of occupation numbers.