Scaling Behavior of Ricci Curvature at Short Distance near Two Dimensions

TL;DR

This paper investigates how Ricci curvature behaves at short distances in quantum gravity near two dimensions, suggesting that scale invariance could resolve spacetime singularities like the big bang.

Contribution

It demonstrates the scaling behavior of Ricci curvature in quantum gravity near two dimensions, linking it to potential resolution of spacetime singularities.

Findings

Ricci curvature scales with a definite dimension at short distances

Spacetime singularities may be understood as scaling phenomena

Scale invariance at short distances could resolve singularities

Abstract

We study the renormalization of the Ricci curvature as an example of generally covariant operators in quantum gravity near two dimensions. We find that it scales with a definite scaling dimension at short distance. The Ricci curvature singularity at the big bang can be viewed as such a scaling phenomenon. The problem of the spacetime singularity may be resolved by the scale invariance of the spacetime at short distance.