Perturbation Theory for Path Integrals in Quadratic Gravity

TL;DR

This paper develops a perturbation theory framework for evaluating path integrals in quadratic gravity models within FLRW spacetime, focusing on the dynamical scale factor and its average in the first perturbative order.

Contribution

It introduces a novel perturbative approach for path integrals in quadratic gravity, emphasizing the role of the scale factor as the key dynamical variable.

Findings

Derived the first-order average of the scale factor in quadratic gravity

Established a perturbation method for path integrals with diffeomorphism invariance

Provided a foundation for further quantum cosmology calculations

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.