Strong Coupling Quantum Gravity and Physics beyond the Planck Scale

TL;DR

This paper introduces a new renormalization scheme and a strong coupling expansion for quantum gravity, aiming to explore quantum geometry at scales below the Planck length.

Contribution

It proposes a novel renormalization prescription for the Wheeler-DeWitt equation and develops a strong coupling expansion as an approximation method for quantum gravity.

Findings

Solved the Wheeler-DeWitt equation to second order in the expansion

Identified problems in the proposed approach

Provided local solutions for quantum geometry at sub-Planckian scales

Abstract

We propose a renormalization prescription for the Wheeler-DeWitt equation of (3+1)-dimensional Einstein gravity and also propose a strong coupling expansion as an approximation scheme to probe quantum geometry at length scales much smaller than the Planck length. We solve the Wheeler-DeWitt equation to the second order in the expansion in a class of local solutions and discuss problems arising in our approach.