Wheeler-Dewitt Metric and the Attractivity of Gravity

TL;DR

This paper explores a family of ultralocal metrics in canonical gravity, revealing how their properties influence gravitational behavior and constraining their parameters using primordial helium data.

Contribution

It introduces a parameterized class of ultralocal metrics on gravity's configuration space and analyzes their impact on gravity's nature and observational constraints.

Findings

For certain parameter ranges, gravity becomes repulsive.

The parameter $eta$ is constrained between 0.4 and 0.55 based on helium abundance.

The signature of the metric changes with the parameter value.

Abstract

We investigate the class of ultralocal metrics on the configuration space of canonical gravity. It is described by a parameter $\alpha$, where $\alpha=0.5$ corresponds to general relativity. For $\alpha$ less than a critical value the signature is positive definite, while for all other values it is indefinite. We show that in the positive definite case gravity becomes repulsive. From the primordial helium abundance we find that $\alpha$ must lie between $0.4$ and $0.55$.