Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle

TL;DR

This paper extends Verlinde's entropic gravity framework to include phase-space noncommutativity, deriving bounds on noncommutative parameters through the Equivalence Principle and introducing an effective Planck's constant.

Contribution

It introduces a phase-space noncommutative model into entropic gravity and establishes bounds on noncommutative parameters using the Equivalence Principle.

Findings

Bound on noncommutative parameters derived

Effective Planck's constant emerges from noncommutativity

Generalization of entropic gravity framework

Abstract

We generalize E. Verlinde's entropic gravity reasoning to a phase-space noncommutativity set-up. This allow us to impose a bound on the product of the noncommutative parameters based on the Equivalence Principle. The key feature of our analysis is an effective Planck's constant that naturally arises when accounting for the noncommutative features of the phase-space.