Effective Potential of the Conformal Factor: Gravitational Average Action and Dynamical Triangulations

TL;DR

This paper investigates the effective potential of the conformal factor in Quantum Einstein Gravity, demonstrating that its behavior near the origin indicates asymptotic safety and aligns with numerical simulations in Causal Dynamical Triangulations.

Contribution

It shows, without truncations, that the potential's behavior near the origin signals asymptotic safety, connecting analytical and numerical approaches.

Findings

Potential exhibits characteristic behavior near the origin

Behavior consistent with non-Gaussian UV fixed point

Alignment with numerical simulations in Causal Dynamical Triangulations

Abstract

We discuss the effective potential of the conformal factor in the effective average action approach to Quantum Einstein Gravity. Without invoking any truncation or other approximations we show that if the theory has has a non-Gaussian ultraviolet fixed point and is asymptotically safe the potential has a characteristic behavior near the origin. We argue that this characteristic behavior has already been observed in numerical simulations within the Causal Dynamical Triangulation approach.