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

Abstract

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 non-interacting Bose-Einstein condensate imposes constraints on linear GUP and Palatini $f(R)$ gravity (Eddington-inspired Born-Infeld gravity) within the ranges of $-10^{12}\lesssim \sigma \lesssim 3\times 10^{24}\text{ s}/\text{kg m}$ and $-10^{-1}\lesssim \bar{\beta }\lesssim 10^{11}{\text{ m}}^2$ ($-4\times 10^{-1}\lesssim \epsilon \lesssim 4\times 10^{11}{\text{ m}}^2$), respectively. In contrast, the properties of liquid helium suggest more realistic 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 seismic waves provides improved constraints for quantum and modified gravity by approximately one order of magnitude.

9 pages, 3 figures

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