# Linear growth index of matter perturbations in Rastall gravity

## TL;DR

This paper investigates the evolution of matter perturbations in Rastall gravity, revealing that while background dynamics resemble the ΛCDM model, the growth index at the perturbation level significantly depends on Rastall's parameter, indicating deviations from standard cosmology.

## Contribution

The study analyzes the growth index of matter perturbations in Rastall gravity, highlighting differences from ΛCDM at the perturbation level and clarifying the debate on its equivalence to general relativity.

## Key findings

- Background evolution matches ΛCDM regardless of Rastall's parameter.
- Growth index evolution depends on Rastall's parameter.
- Deviations from ΛCDM are significant at the perturbation level.

## Abstract

Rastall gravity theory shows notable features consistent with physical observations in comparison to the standard Einstein theory. Recently, there has been a debate about the equivalence of Rastall gravity and general relativity. Motivated by this open issue, in the present work, we attempt to shed some light on this debate by analyzing the evolution of the Rastall based cosmological model at the background as well as perturbation level. Employing the dynamical system techniques, we found that at late times, the dynamics of the model resembles the $\Lambda$CDM model at the background level irrespective of the choice of Rastall's parameter. However, at the perturbation level, we found that the evolution of the growth index heavily depends on the Rastall's parameter and displays a significant deviation from the $\Lambda$CDM model.