Implementing Markov's Limiting Curvature Hypothesis

TL;DR

This paper reviews recent work on effective gravitational actions that limit curvature, potentially resolving singularities in space-time and early universe cosmology by making solutions nonsingular and asymptotically free.

Contribution

It introduces a class of effective gravitational actions where all symmetric solutions have bounded curvature, addressing singularities and asymptotic freedom in high-curvature regimes.

Findings

Solutions with sufficient symmetry are nonsingular due to limiting curvature.

Near the limiting curvature, matter-gravity coupling vanishes, indicating asymptotic freedom.

The approach impacts understanding of space-time singularities and early universe behavior.

Abstract

The effective action for gravity at high curvatures is likely to contain higher derivative terms. These corrections may have profound consequences for the singularity structure of space-time and for early Universe cosmology. In this contribution, recent work is reviewed which demonstrates that it is possible to construct a class of effective gravitational actions for which all solutions with sufficient symmetries have limited curvature and are nonsingular. Near the limiting curvature, the coupling between matter and gravity goes to zero and in this sense the theory is asymptotically free.