Modified gravity emerging from thermodynamics and holographic principle

TL;DR

This paper explores how modifications to entropy laws from quantum effects and extra dimensions influence gravity, leading to new formulations of Newton's law and cosmological equations that can explain the universe's accelerated expansion.

Contribution

It introduces modified gravity theories derived from altered entropy-area relations based on holography and thermodynamics, extending Verlinde's entropic gravity framework.

Findings

Modified Newton's law and Friedmann equations derived

De-Sitter solutions obtained from modified entropy laws

Potential explanation for cosmic acceleration as an emergent phenomenon

Abstract

A new conception is proposed in Ref.\cite{Verlinde:2010hp,Padmanabhan:2009kr} that gravity is one kind of entropic force. In this letter, we try to discuss its applications to the modified gravities by using three different corrections to the area law of entropy which are derived from the quantum effects and extra dimensions. According to the assumption of holographic principle, the number of bits $N$ which is related to the equipartition law of energy is modified. Then, the modified law of Newton's gravity and the modified Friedmann equations are obtained by using the new notion. By choosing suitable parameters, the modified area law of entropy leads to de-Sitter solutions which can be used to explain the accelerating expansion of our universe. It suggests that the accelerating phase in our universe may be an emergent phenomenon based on holographic principle and thermodynamics.