Path integral measure in quadratic gravity models

We propose to consider the cumbersome actions in some theories as the sophisticated actions for a true dynamical variable leading to the Gaussian functional measures. We consider path integrals in 4D Quadratic Gravity in FLRW metric as the integrals over the functional measure µ(g) = exp {−A2} dg , where A2 is the part of the action quadratic in R, and g(τ) is the dynamical variable invariant under the group of diffeomorphisms of the time coordinate τ. 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. In a model of 2D gravity with the action quadratic in curvature, we represent path integrals as integrals over the SL(2, R) invariant Gaussian functional measure and reduce them to the products of Wiener path integrals. As an example, we calculate the correlation function of the metric in the first perturbative order.