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

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.

10 pages. Version accepted for publication in Universe

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