Implications of the Generalized Entropy Formalisms on the Newtonian Gravity and Dynamics

TL;DR

This paper explores how generalized entropy formalisms, when applied via Verlinde's hypothesis, modify Newtonian gravity and potentially unify explanations for dark matter, dark energy, and cosmic acceleration.

Contribution

It derives new modifications to Newtonian gravity based on generalized entropy measures and links these to MOND and cosmic acceleration phenomena.

Findings

Generalized entropy measures can modify Newtonian gravity.

These modifications support MOND-like dynamics.

They may unify explanations for dark sectors of the universe.

Abstract

Employing the Verlinde's hypothesis, and considering two well-known generalized entropy formalisms, two modifications to the Newtonian gravity are derived. In addition, it has been shown that the generalized entropy measures may also provide theoretical basis for the Modified Newtonian Dynamics (MOND) theory and generate its modified forms. Since these entropy measures are also successful in describing the current accelerated universe, our results indicate that the origin of dark sectors of cosmos may be unified to meeting the generalized entropy measures instead of the Boltzmann-Gibbs entropy by the gravitational systems due to the long-range nature of gravity.