Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization

TL;DR

This paper investigates the renormalization group flow of f(R) gravity using exponential parametrization and physical gauge fixing, finding scaling solutions and fixed points that inform quantum gravity models.

Contribution

It introduces a novel approach with exponential parametrization and a physical gauge fixing to derive a functional flow equation for f(R) gravity, identifying new fixed points and solution behaviors.

Findings

Found simple quadratic polynomial solutions for certain parameters.

Discovered global solutions with two relevant directions.

Analyzed the parameter space for extending solutions.

Abstract

We employ the exponential parametrization of the metric and a "physical" gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an $f(R)$ truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function $f$. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure.