Unveiling Phase Space Modifications: A Clash of Modified Gravity and the Generalized Uncertainty Principle

TL;DR

This paper investigates the relationship between Modified Gravity theories and phase space volume modifications, deriving bounds on parameters and establishing a connection with the Generalized Uncertainty Principle to enable experimental tests.

Contribution

It introduces a novel link between Modified Gravity models and the Generalized Uncertainty Principle, deriving bounds and enabling experimental testing of gravity proposals.

Findings

Derived bounds on GUP parameter sigma: -6×10^{22} to 3×10^{22} s/kg m

Established lower bounds for Palatini f(R) gravity: beta > -7.51587×10^7 m^2

Set bounds for Eddington-inspired Born-Infeld gravity: epsilon > -1.88×10^7 m^2

Abstract

This study explores the link between Modified Gravity and modifications of phase space volume. Analyzing Fermi gas modifications {in the non-relativistic limit of the} Ricci-based gravities, we derive a generalized partition function in the grand-canonical ensemble, connecting Modified Gravity models with the Generalized Uncertainty Principle. Using this correspondence, we also establish bounds on the linear Generalized Uncertainty Principle: $-6\times10^{22}\lesssim\sigma\lesssim 3\times 10^{22}{\text{ s}}/{\text{kg m}}$, as well as lower bounds for Palatini $f(R)$ gravity $\beta > -7.51587\times 10^7 \text{ m}^2$ and Eddington-inspired Born-Infeld gravity $\epsilon > -1.88\times 10^7 \text{ m}^2$, ensuring microscopic stability. This connection also facilitates testing gravity proposals through tabletop experiments.