Entropic Corrections to Friedmann Equations

TL;DR

This paper explores how quantum corrections to black hole entropy influence entropic gravity, leading to modified Newtonian and Friedmann equations, thus supporting the universality of log corrections within Verlinde's emergent gravity framework.

Contribution

It derives corrected gravitational and cosmological equations using quantum-modified entropy, extending Verlinde's entropic gravity model with new quantum insights.

Findings

Quantum entropy corrections modify Newton's law.

Modified Friedmann equations incorporate quantum effects.

Supports universality of log entropy corrections.

Abstract

Recently, Verlinde discussed that gravity can be understood as an entropic force caused by changes in the information associated with the positions of material bodies. In the Verlinde's argument, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. In this note, by employing this modified entropy-area relation, we derive corrections to Newton's law of gravitation as well as modified Friedman equations by adopting the viewpoint that gravity can be emerged as an entropic force. Our study further supports the universality of the log correction and provides a strong consistency check on Verlinde's model.