Gauge fixing in cosmological perturbations of Unimodular Gravity

TL;DR

This paper explores gauge fixing in cosmological perturbations within Unimodular Gravity, demonstrating the consistent fixing of Newtonian and Synchronous gauges and analyzing their implications on matter perturbations and observable effects.

Contribution

It shows for the first time that both gauges can be fixed consistently in Unimodular Gravity, highlighting differences from General Relativity in scalar mode dynamics and gauge conditions.

Findings

Both gauges can be fixed consistently in Unimodular Gravity.

The unimodular constraint reduces scalar degrees of freedom to one.

Differences in gauge conditions affect the density contrast and Sachs-Wolfe effect.

Abstract

With focus on the cosmological evolution of linear perturbations of matter and geometry, we calculate the equivalent expressions to that of the Newtonian and Synchronous gauges within the framework of Unimodular Gravity, being these two gauges commonly used and implemented in Boltzmann codes. An important aspect of our analysis is the inclusion of the energy-momentum current violation, as well as its perturbations. Moreover, for the first time we demonstrate that it is possible to fix both gauges consistently, although as it has been already noticed in previous literature, neither of them is recovered in the sense of the dynamics given in General Relativity for matter and metric fluctuations. Specifically, we show that since the unimodular constraint at the level of linear perturbations lead to only one degree of freedom of scalar modes of metric fluctuations, the dynamics in Unimodular Gravity forces to keep the anisotropic stress in the Newtonian gauge, whereas the cold dark matter comoving frame can not be set in the Synchronous gauge. The physical implications on the density contrast of cold dark matter is reviewed, and the Sachs-Wolfe effect is obtained and compared with previous results in the literature of cosmological perturbations in Unimodular Gravity.