  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.

General Relativity and Quantum Cosmology