Growth of perturbations in Tsallis and Barrow cosmology

We report the effects of entropic corrections to the Friedmann equations on the growth of perturbations in the early stages of the universe. We consider two types of corrections to the area law of entropy, known as Tsallis and Barrow entropy. Using these corrections to entropy, we derive the modified Friedmann equations and explore the growth of perturbations in a flat universe filled with dark matter (DM) and the cosmological constant. We employ the spherically symmetric collapse formalism and work in the linear regime for the perturbations. Interestingly enough, we find that the profile of density contrast is quite different from the standard cosmology in Tsallis and Barrow cosmology. We observe that the growth rate of matter perturbations crucially depends on the values of Tsallis and Barrow parameters. By increasing these entropy correction parameters, the total density contrast increases as well. This implies that perturbations grow faster in a universe with modified entropy-corrected Friedmann equations.