Linear growth index of matter perturbations in Rastall gravity

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.