Mass gap in non-perturbative quadratic $\mathcal{R}^2$ gravity via Dyson-Schwinger

TL;DR

This paper uses Dyson-Schwinger equations to analyze a quadratic Ricci scalar gravity model, revealing a mass gap that depends on the Ricci scalar and affects low-energy scalar interactions.

Contribution

It introduces a novel application of Dyson-Schwinger equations to quadratic Ricci scalar gravity, demonstrating the emergence of a Ricci scalar-dependent mass gap.

Findings

Mass gap increases with the square root of Ricci scalar

Scalar sector becomes ineffective at low energies

Higgs-like solutions with finite mass are found

Abstract

We apply in a simple model derived from quadratic $\mathcal{R}^2$ gravity the technique of Dyson-Schwinger equations to solve for its corresponding quantum theory. Particularly, we solve the classical equations of motion to get a solution to the hierarchy of Dyson-Schwinger equations in the limit of large Ricci scalar, assumed to be constant and larger than the square of the Starobinsky mass. Moving to the Einstein frame, the model admits Higgs-like solutions with a single particle having a finite mass. We quantize the scalar field showing the appearing of a mass gap through a Higgs-like solution. The presence of the mass gap, that increases with the square root of the Ricci scalar, shows how the effect of the scalar sector at low-energy becomes ineffective, making it relevant only at short distances.