Locally Scale-Invariant Gravity

TL;DR

This paper proposes a gravity theory invariant under local scale transformations, extending general relativity to include Weyl invariance and internal symmetries, with implications for cosmological models like FRW spacetime.

Contribution

It introduces a Weyl-invariant scalar-tensor extension of GR that incorporates local scale invariance and internal symmetries, providing a new perspective on gravitational interactions.

Findings

Reformulation of FRW spacetime in WIST form with static space and evolving masses.

Reduction to Weyl-invariant GR under isotropic deformations.

Connection between global charges and gravitational sourcing.

Abstract

We put forward the idea that in addition to diffeomorphism invariance of general relativity (GR) the gravitational interaction is invariant under arbitrary scale-deformations of the metric field. In addition, we assume that the scaling field has an internal symmetry. The global charges that are associated with this symmetry could potentially source the gravitational field. In the case that isotropic deformations are considered, the theory reduces to a Weyl-invariant (WI) version of GR. In the case that Minkowski spacetime is deformed the vierbein formalism is recovered, rendering GR a field theory on Minkowski spacetime. A few implications of a classical Weyl-invariant scalar-tensor (WIST) generalization of general relativity (GR) are considered. As an example, we recast the homogeneous and isotropic Friedmann-Robertson-Walker (FRW) spacetime in the WIST form with static space and monotonically evolving masses.