A Theory for the Conformal Factor in Quantum $R^2$ Gravity

TL;DR

This paper develops a new theoretical framework for the conformal factor in quantum R^2 gravity, deriving the effective potential and proposing a mechanism for Einstein gravity emergence at large scales.

Contribution

It introduces a novel one-loop renormalization group approach to quantum R^2 gravity and explicitly computes the effective potential for the conformal factor.

Findings

Explicit one-loop effective potential for the conformal factor

Proposed mechanism for Einstein gravity emergence

Comparison with conformal anomaly induced effective theory

Abstract

A new theory for the conformal factor in R$^2$-gravity is developed. The infrared phase of this theory, which follows from the one-loop renormalization group equations for the whole quantum R$^2$-gravity theory is described. The one-loop effective potential for the conformal factor is found explicitly and a mechanism for inducing Einstein gravity at the minimum of the effective potential for the conformal factor is suggested. A comparison with the effective theory of the conformal factor induced by the conformal anomaly, and also aiming to describe quantum gravity at large distances, is done.