Using cosmological perturbation theory to distinguish between General Relativity and Unimodular Gravity

TL;DR

This paper investigates whether Unimodular Gravity and General Relativity can be distinguished through classical scalar perturbations in cosmology, especially when a non-minimal scalar field is present, revealing differences at the perturbative level.

Contribution

The study provides a detailed analysis of scalar perturbations in Unimodular Gravity, highlighting differences from General Relativity when a non-minimal scalar field is included.

Findings

Unimodular Gravity and General Relativity are not fully equivalent at the perturbative level.

Differences emerge in scalar perturbations when a non-minimal scalar field is introduced.

Classical perturbation analysis can distinguish between the two theories.

Abstract

Unimodular Gravity is one of the oldest geometric gravity theory alternative to General Relativity. Essentially, it is based on the Einstein-Hilbert Lagrangian with an additional constraint on the determinant of the metric. It can be explicitly shown that Unimodular Gravity can be recast as General Relativity in presence of a cosmological constant. This fact has led to many discussions on the equivalence of both theories at classical and quantum levels. Here we present an analysis focused on the classical scalar perturbations around a cosmological background. The discussion is extended for the case where a non-minimal coupled scalar field is introduced. Our results indicate that the equivalence is not verified completely at perturbative level.