Review of strongly coupled regimes in gravity with Dyson-Schwinger approach

TL;DR

This paper applies Dyson-Schwinger equations to analyze strongly coupled gravity theories with de-Sitter, quadratic curvature, and scalar couplings, identifying conformally flat solutions and cosmological phase transitions.

Contribution

It introduces a Dyson-Schwinger approach to quantum gravity theories with specific solutions and explores their cosmological implications.

Findings

Identification of conformally flat metric solutions in gravity theories.

Sequence of cosmological phase transitions related to conformal invariance breaking.

Non-minimal coupling can hinder conformal invariance breaking.

Abstract

We analyze various gravity theories involving de-Sitter, quadratic $\mathcal{R}^2$ and non-minimally coupled scalar in the light of application of the Dyson-Schwinger technique involving exact background solution of the Green's function. We denote specific set of solutions for the metric to move towards a quantum analysis of the theory. This kind of solutions is identified as conformally flat metric. Such a conclusion naturally arises in the use of the Dyson-Schwinger equations in the study of the Yang-Mills theory through the mapping theorem. We show a sequence of cosmological phase transitions starting from the breaking of such conformal invariance that can be hindered by the presence of the non-minimal coupling.