Path Integrals in Quadratic Gravity

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 $\int\,F(g)\,\exp\left\{-A \right\}dg$ as the integrals over the functional measure $μ(g)=\exp\left\{-A_{2} \right\}dg\,,\$ where $A_{2}$ is the part of the action $A$ quadratic in $R\,.$ The rest part of the action stands in the exponent 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.

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