Perturbation Theory for Path Integrals in Quadratic Gravity

The action $A$ of Quadratic Gravity in FLRW metric is invariant under the group of diffeomorphisms of the time coordinate and can be written in terms of the only dynamical variable $g(\tau )\mathrm{.}$ We construct perturbation theory for calculating path integrals of the form $\int F(g)\exp \{-A(g)\}dg,$ and find the averaged value of the scale factor in the first nontrivial perturbative order.