Observational constraints on Rastall's cosmology

TL;DR

This paper tests Rastall's modified gravity theory using supernova data, finding it consistent only when it reduces to General Relativity, especially for stable cosmological perturbations.

Contribution

It provides observational constraints on Rastall's theory in cosmology and analyzes the stability of perturbations within this framework.

Findings

Bayesian analysis prefers $w_x$ close to -1.

Perturbations are unstable if $w_x eq -1$ and $ eq 1$.

General Relativity remains the stable and favored theory.

Abstract

Rastall's theory is a modification of General Relativity, based on the non-conservation of the stress-energy tensor. The latter is encoded in a parameter $\gamma$ such that $\gamma = 1$ restores the usual $\nabla_\nu T^{\mu\nu} = 0$ law. We test Rastall's theory in cosmology, on a flat Robertson-Walker metric, investigating a two-fluid model and using the type Ia supernovae Constitution dataset. One of the fluids is pressureless and obeys the usual conservation law, whereas the other is described by an equation of state $p_x = w_x\rho_x$, with $w_x$ constant. The Bayesian analysis of the Constitution set does not strictly constrain the parameter $\gamma$ and prefers values of $w_x$ close to -1. We then address the evolution of small perturbations and show that they are dramatically unstable if $w_x \neq -1$ and $\gamma \neq 1$, i.e. General Relativity is the favored configuration. The only alternative is $w_x = -1$, for which the dynamics becomes independent from $\gamma$.