Unveiling phase space modifications: A clash of modified gravity and the generalized uncertainty principle
Aneta Wojnar
Abstract
This study explores the link between modified gravity and modifications of phase space volume. Analyzing Fermi gas modifications in the nonrelativistic 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: $\ensuremath{-}6\ifmmode\times\else\texttimes\fi{}{10}^{22}\ensuremath{\lesssim}\ensuremath{\sigma}\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}{10}^{22}\text{ }\text{ }\mathrm{s}/\mathrm{kg}\text{ }\mathrm{m}$, as well as lower bounds for Palatini $f(R)$ gravity $\ensuremath{\beta}>\ensuremath{-}7.51587\ifmmode\times\else\texttimes\fi{}{10}^{7}\text{ }\text{ }{\mathrm{m}}^{2}$ and Eddington-inspired Born-Infeld gravity $\ensuremath{\epsilon}>\ensuremath{-}1.88\ifmmode\times\else\texttimes\fi{}{10}^{7}\text{ }\text{ }{\mathrm{m}}^{2}$, ensuring microscopic stability. This connection also facilitates testing gravity proposals through tabletop experiments.