Dynamics of the conformal factor in 4D gravity

TL;DR

This paper proposes that quantum fluctuations of the conformal factor significantly alter 4D gravity at large distances, leading to a scale-invariant phase that could address the cosmological constant problem.

Contribution

It introduces an effective scalar theory for the conformal factor, induced by trace anomaly, with a non-trivial infrared fixed point in 4D gravity.

Findings

Infrared quantum fluctuations modify 4D gravity at large scales.

The effective theory is renormalizable and exhibits a scale-invariant phase.

Potential implications for solving the cosmological constant problem.

Abstract

We argue that 4D gravity is drastically modified at distances larger than the horizon scale, due to the large infrared quantum fluctuations of the conformal part of the metric. The infrared dynamics of the conformal factor is generated by an effective action, induced by the trace anomaly of matter in curved space, analogous to the Polyakov action in two dimensions. The resulting effective scalar theory is renormalizable, and possesses a non-trivial, infrared stable fixed point, characterized by an anomalous scaling dimension of the conformal factor. We argue that this theory describes a large distance scale invariant phase of 4D gravity and provides a framework for a dynamical solution of the cosmological constant problem.