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

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: -6x10(22) less than or similar to sigma less than or similar to 3x 10(22) s/kg m, as well as lower bounds for Palatini f(r) gravity beta >-7.51587 x 10(7) m(2) and Eddington-inspired Born-Infeld gravity epsilon > -1.88 x 10(7) m(2), ensuring microscopic stability. This connection also facilitates testing gravity proposals through tabletop experiments.