A flow equation for f(R) gravity and some of its exact solutions

TL;DR

This paper derives a new RG flow equation for f(R) gravity using exponential parametrization and gauge choices, identifying fixed points with quadratic f(R) forms and exploring parameter-dependent solutions.

Contribution

It introduces a modified RG equation for f(R) gravity considering specific parametrization and gauge, revealing fixed points with quadratic solutions and parameter-dependent behaviors.

Findings

Existence of fixed points with quadratic f(R) forms.

Discrete parameter choices lead to fixed points.

Solutions deform continuously with parameter variations.

Abstract

We write a Renormalization Group (RG) equation for the function f in a theory of gravity in the f(R) truncation. Our equation differs from previous ones due to the exponential parametrization of the quantum fluctuations and to the choice of gauge. The cutoff procedure depends on three free parameters, and we find that there exist discrete special choices of parameters for which the flow equation has fixed points where f=f_0+f_1 R+f_2 R^2. For other values of the parameters the solution seems to be continuously deformed.