Path Integrals in Quadratic Gravity

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 $g(\tau ).$ We propose to consider the path integrals $\int F(g)\exp \left\{-A\right\}dg$ as the integrals over the functional measure $\mu (g)=\exp \left\{-A_2\right\}dg,$ 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 $\mu (g)$ to be equivalent to the Wiener measure, and, as an example, calculate the averaged scale factor in the first nontrivial perturbative order.

19 pages

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