Utilizing the recently established connection between Palatini-like gravity and linear generalized uncertainty principle (GUP) models, we have formulated an approach that facilitates the examination of Bose gases. Our primary focus is on the ideal Bose-Einstein condensate and liquid helium, chosen as illustrative examples to underscore the feasibility of tabletop experiments in assessing gravity models. The noninteracting Bose-Einstein condensate imposes constraints on linear GUP and Palatini $f(R)$ gravity (Eddington-inspired Born-Infeld gravity) within the ranges of -10¹²σ3×10²⁴ s/kg m and -10^-1β10¹¹ m² (${-}4×{}{10}^{{-}1}{}{ε}{}4×{}{10}¹¹ {m}²$), respectively. In contrast, the properties of liquid helium suggest more realistic bounds, specifically ${-}{10}²³{}{σ}{}{10}²³ s/kg m$ and ${-}{10}⁹{}{{β}}{}{10}⁹ {m}²$. Additionally, we argue that the newly developed method employing Earth seismic waves provides improved constraints for quantum and modified gravity by approximately one order of magnitude.
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Aneta Wojnar (2024) studied this question.