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Utilizing the recently established connection between Palatini-like gravityand linear Generalized Uncertainty Principle (GUP) models, we have formulatedan approach that facilitates the examination of Bose gases. Our primary focusis on the ideal Bose-Einstein condensate and liquid helium, chosen asillustrative examples to underscore the feasibility of tabletop experiments inassessing gravity models. The non-interacting Bose-Einstein condensate imposesconstraints on linear GUP and Palatini $f(R)$ gravity (Eddington-inspiredBorn-Infeld gravity) within the ranges of $-10^{12}\lesssim\sigma\lesssim3\times 10^{24}{\text{ s}}/{\text{kg m}}$ and$-10^{-1}\lesssim\bar\beta\lesssim 10^{11} \text{ m}^2$($-4\times10^{-1}\lesssim\epsilon\lesssim 4\times 10^{11} \text{ m}^2$),respectively. In contrast, the properties of liquid helium suggest morerealistic bounds, specifically $-10^{23}\lesssim\sigma\lesssim 10^{23}{\text{s}}/{\text{kg m}}$ and $-10^{9}\lesssim\bar\beta\lesssim 10^{9} \text{ m}^2$.Additionally, we argue that the newly developed method employing Earth seismicwaves provides improved constraints for quantum and modified gravity byapproximately one order of magnitude.

Bose-Einstein Condensate and Liquid Helium He$^4$: Implications of GUP and Modified Gravity Correspondence