Growth of Perturbations in Tsallis and Barrow Cosmology

Abstract

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.

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$

“…This entropy model has later been considered as a model for holographic dark energy [387,388] (see also Refs. [389][390][391][392][393][394][395][396][397][398][399][400][401][402][403][404][405][406][407][408]). In the toy model considered, a three-dimensional FIG.…”

Sign Switching Dark Energy from a Running Barrow Entropy

“…However the "bare" gravitational constant G that appears at the level of the action is not the same as the effective G eff that appears in the modified Friedmann equation Eq. (10). Also, the Barrow entropy itself contains A 0 = 4G, which is the "bare" G. The fact that the G eff is smaller in the early universe could suggests that we may be able to ameliorate the arrow of time problem [41][42][43][44][45][46][47][48][49][50] following the same line of thought of Greene et.…”

“…Typically, the effective gravitational constant that governs structure formation may not be the same as the G eff that appears in the background Friedmann equation, which may also differ from the "bare" G. A concrete example is provided in [53]. Structure formation in the case of fixed BEI has been recently studied in [10]. In fact, a varying gravitational constant would cause many issues and early time cosmology would need to be re-examined in close details [54] (for example, CMB angular power spectrum would be modified [40,54]).…”

“…In this work, we will argue that δ has to be a function of energy scale and study the implications of Barrow entropy to cosmology (by the expansion of the universe, δ is thus a function of cosmic time). Such a possibility was also raised in [7,10]. We expect that, as quantum gravitational effects become more pronounced near the Big Bang, δ → 1.…”

Sign Switching Dark Energy from a Running Barrow Entropy

“…In this work, we argue that δ has to be a function of the energy scale and study the implications of Barrow entropy for cosmology (by the expansion of the universe, δ is thus a function of cosmic time). Such a possibility was also raised in [7,10,11]. We expect that, as quantum gravitational effects become more pronounced near the Big Bang, δ → 1.…”