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 energy (DE) and dark matter (DM). We employ the spherically symmetric collapse formalism and work in the liner regime for the perturbations. We first consider the constant equation of state (EoS) parameter for the DE and then extend our study to the variable EoS parameter for DE. Interstingly enough, we find out that the profile of density contrast quite differs from the standard cosmology. We observe that the growth rate of matter perturbations crucially depend on the values of Tsallis and Barrow parameters. With increasing the 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.

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.

Mimetic theory of gravity was proposed as an alternative description for the dark matter (DM) puzzle. It was argued that the mimetic field can encode a dynamical longitudinal degree of freedom which can play the role of mimetic DM. In this paper, we disclose the effects of an extra longitudinal degree of freedom on the evolution of perturbations in the framework of mimetic gravity. We consider a flat Friedmann-Robertson-Walker (FRW) background and explore the linear perturbations by adopting the spherically symmetric collapse formalism. By suitably choosing the potential of the mimetic field, we are able to solve the perturbed field equations in the linear regime and derive the density contrast δm in terms of the redshift parameter z. We observe that δm starts growing from its initial value at the early stages of the universe and as the universe expands, it grows slower compared to the standard cosmology. This may due to the extra degree of freedom of the gravitational field which affects the growth of perturbations. We then consider the effects of this potential on the density abundance and the deceleration parameter. We find out that mimetic potential can play the role of dark energy (DE) and affects the dynamics of matter perturbations and cosmological parameters.

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We explore the influences of the higher order Gauss-Bonnet (GB) correction terms on the growth of perturbations at the early stage of the universe. We consider a Friedmann-Robertson-Walker (FRW) background in the presence a cosmological constant, and study the linear perturbations by adopting the spherically symmetric collapse (SC) formalism. We disclose the role of the GB coupling parameter α, as well as the extra dimension on the growth of perturbations. We find that the matter density contrast starts growing at the early stages of the universe and, as the universe expands, it grows faster compared to the Einstein gravity. Besides, in the framework of GB gravity, the growth of matter perturbations in higher dimensions is faster than four-dimensions. Further, the growth of perturbations increases with increasing the GB coupling parameter α. This is an expected result, since the higher order GB correction terms increase the strength of the gravity and thus support the growth of perturbations. Finally, we explore the behavior of the density abundance, the deceleration parameter and jerk parameter of this model.