Review of Strongly Coupled Regimes in Gravity with Dyson–Schwinger Approach

We analyze various gravity theories involving de Sitter, quadratic R2 and non-minimally coupled scalar backgrounds in the light of the application of the Dyson–Schwinger technique involving an 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 solution is identified as a 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.