New explanation for accelerated expansion and flat galactic rotation curves

TL;DR

This paper proposes a modified gravity model based on Tsallis entropy that explains cosmic acceleration and flat galactic rotation curves without dark energy or dark matter, by altering gravitational laws on large scales.

Contribution

It introduces a novel approach using non-additive Tsallis entropy to modify gravitational equations, providing alternative explanations for dark energy and dark matter phenomena.

Findings

Modified Friedmann equation predicts accelerated expansion with ordinary matter.

Modified Newton's law explains flat galactic rotation curves without dark matter.

The model links the non-extensive parameter to cosmological and galactic phenomena.

Abstract

Employing the non-additive Tsallis entropy, $S\sim A^{\beta}$, for the large-scale gravitational systems, we disclose that in the cosmological scales both Friedmann equation and the equation of motion for the Newtonian cosmology get modified, accordingly. We then derive the modified Newton's law of gravitation which is valid on the large scales. We show that, in the relativistic regime, the modified Friedmann equation admits an accelerated expansion, for a universe filled with ordinary matter, without invoking any kind of dark energy, provided the non-extensive parameter is chosen $\beta<1/2$. In the non-relativistic regime, however, the modified Newton's law of gravitation can explain the flat galactic rotation curves without invoking particle dark matter provided $\beta \lesssim1/2$. Our study may be regarded as an alternative explanation for the "dark side of the universe", through modification of the gravitational field equations.