Growth of Perturbations in Tsallis and Barrow Cosmology

We disclose the effects of the 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 entropies. 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 cosmological constant. We employ the spherically symmetric collapse formalism and work in the linear regime for the perturbations. Interestingly enough, we find out that the profile of density contrast quite differs from the standard cosmology in Tsallis and barrow cosmology. We observe that the growth rate of matter perturbations crucially depend on the values of Tsallis and Barrow parameters. With increasing these correction parameters to the entropy, the total density contrast increases as well. This implies that perturbations grow up faster in a universe with modified entropy corrected Friedmann equations.