Perturbation Theory for Path Integrals in Quadratic Gravity

Abstract: 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 $g(\tau)\,.$ We construct perturbation theory for calculating path integrals of the form $\int\,F(g)\,\exp\left{-A (g)\right}dg\,,$ and find the averaged value of the scale factor in the first nontrivial perturbative order.