Scale-invariance in gravity and implications for the cosmological constant

TL;DR

This paper explores a scale-invariant gravity theory with conformal symmetry, addressing issues in the original formulation and proposing a new, highly restrictive theory that offers potential solutions to the cosmological constant problem.

Contribution

The authors develop a new scale-invariant gravity theory that resolves the universe volume problem and offers testable predictions, including a novel approach to the cosmological constant.

Findings

New theory has attractive features for quantisation and cosmology

Resolves the volume of universe as a dynamical variable

Offers potential solutions to the cosmological constant problem

Abstract

Recently a scale invariant theory of gravity was constructed by imposing a conformal symmetry on general relativity. The imposition of this symmetry changed the configuration space from superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms - to conformal superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. However, despite numerous attractive features, the theory suffers from at least one major problem: the volume of the universe is no longer a dynamical variable. In attempting to resolve this problem a new theory is found which has several surprising and atractive features from both quantisation and cosmological perspectives. Furthermore, it is an extremely restrictive theory and thus may provide testable predictions quickly and easily. One particularly interesting feature of the theory is the resolution of the cosmological constant problem.