Path integrals in quadratic gravity

Abstract

Abstract Using the invariance of Quadratic Gravity in FLRW metric under the group of diffeomorphisms of the time coordinate, we rewrite the action A of the theory in terms of the invariant dynamical variable g(τ).We propose to consider the path integrals ∫F(g) exp {−A}dg as the integrals over the functional measure μ(g) = exp {−A2}dg, where A2 is the part of the action A quadratic in R. The rest part of the action in the exponent stands in the integrand as the “interaction” term. We prove the measure μ(g) to be equivalent to the Wiener measure, and, as an example, calculate the averaged scale factor in the first nontrivial perturbative order.