Infrared behavior of Weyl Gravity: Functional Renormalization Group approach

TL;DR

This paper investigates the infrared behavior of quantum Weyl gravity using the functional renormalization group, revealing a dynamical scale symmetry breaking, an IR fixed point, and bouncing RG flow, with potential implications for cosmology.

Contribution

It introduces a novel analysis of Weyl gravity's IR regime via RG flow on specific backgrounds, highlighting scale symmetry breaking and bouncing behavior.

Findings

Identification of a genuine IR fixed point at zero scale

Observation of bouncing behavior in the RG flow

IR fixed point is IR-stable with computed scaling dimensions

Abstract

Starting from an ultraviolet fixed point, we study the infrared behavior of quantum Weyl gravity in terms of a functional renormalization group (RG) flow equation. To do so, we employ two classes of Bach-flat backgrounds, namely maximally symmetric spacetimes and Ricci-flat backgrounds in the improved one-loop scheme. We show that in the absence of matter fields and with a topological term included, the effective action exhibits dynamical breaking of scale symmetry. In particular, it is shown that apart from a genuine IR fixed point that is reached at a zero-value of the running scale, the RG flow also exhibits bouncing behavior in the IR regime. We demonstrate that both $\beta_C$ and $\beta_E$ reach the RG turning point (almost) simultaneously at the same finite energy scale, irrespectively of the chosen background. The IR fixed point itself is found to be IR-stable in the space of the considered couplings. Ensuing scaling dimensions of both operators are also computed. Salient issues, including the connection of the observed bouncing RG flow behavior with holography and prospective implications in early Universe cosmology, are also briefly discussed.