Growth of perturbations in Tsallis and Barrow cosmology

Abstract

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.

Barrow holographic dark energy in Brane world cosmology

“…The BHDE parameter, on the other hand, ∆ has to satisfy a theoretical bound 0 ⩽ ∆ ⩽ 1. A recent study [61] also shows considerable deviation in the growth of perturbation in THDE and BHDE despite the similarity of the modified Friedman equations in both the cases. As suggested in [61], this dissimilarity probably originates from the difference in the theoretically allowed range of THDE and BHDE.…”

“…A recent study [61] also shows considerable deviation in the growth of perturbation in THDE and BHDE despite the similarity of the modified Friedman equations in both the cases. As suggested in [61], this dissimilarity probably originates from the difference in the theoretically allowed range of THDE and BHDE. Despite the apparent similarity of the field equations, two significant reasons underlie the current study.…”

“…There is a lack of consensus on the range of THDE parameter (δ) in the literature apart from the fact that for δ = 1 THDE reduces to standard HDE. For example, in [60] δ > 2 is used in many instances where as in [61] THDE parameter (β in the paper) is argued to be < 2. Observational constraints on the THDE parameter [45] while considering Hubble horizon as cut off is 2.211 +0.121 −.181 .…”

Constraining barrow entropy-based cosmology with power-law inflation

“…This is an important testing ground to discriminate among existing modified cosmological models. Preliminary investigation in this direction has been proposed in [ 58 ] in the context of both Tsallis and Barrow entropies, showing that the entropic deformation parameter significantly influences the growth of perturbations. Moreover, one can attempt to extend the present considerations to Cosmology based on other deformed entropies, such as Tsallis entropy with or without radiation sector [ 59 ], Kaniadakis entropy [ 60 ], which is a self-consistent relativistic generalization of Boltzmann–Gibbs entropy with non-trivial cosmological implications [ 61 ], Rényi [ 62 ] or Sharma-Mittal [ 63 ] entropy, which both arise in the context of information theory.…”

Structure Formation in Gauss-Bonnet Gravity

“…Our work differs from [17] in that instead of using the Newtonian gauge, we use SC formalism [55] to examine the evolution of perturbations, which is an appropriate approach to investigate the growth of perturbations and structure formation. In this approach one considers a uniform and spherical symmetric perturbation in an expanding background and describes the growth of perturbations in a spherical region using the same Friedmann equations for the underlying theory of gravity [56][57][58][59][60]. Our work also differs from [61] in that the authors of [61] considered a varying cosmological constant in 4D GB gravity, while we consider the growth of perturbations in higher dimensional GB gravity.…”