The Friedmann equation in modified entropy-area relation from entropy force

TL;DR

This paper explores how modifications to the entropy-area relation, inspired by the holographic principle and the Debye model, lead to corrected Friedmann equations and gravitational laws.

Contribution

It introduces a refined entropy-area relation and derives modified Friedmann and Einstein equations incorporating entropy corrections.

Findings

Derived corrected Newton's laws and Einstein equations.

Obtained modified Friedmann equations for the FRW universe.

Proposed a more precise entropy-area relation in holographic systems.

Abstract

According to the formal holographic principle, a modification to the assumption of holographic principle in Verlinder's investigation of entropy force is obtained. A more precise relation between entropy and area in the holographic system is proposed. With the entropy corrections to the area-relation, we derivate Newton's laws and Einstein equation with a static spherically symmetric holographic screen. Furthermore we derived the correction terms to the modified Friedmann equation of the FRW universe starting from the holographic principle and the Debye model.