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

TL;DR

This paper explores how Bose-Einstein condensates and liquid helium can be used in tabletop experiments to test gravity models and generalized uncertainty principles, providing new bounds on these theories.

Contribution

It introduces a novel approach linking GUP and modified gravity with Bose gases, and derives experimental constraints from condensates and seismic data.

Findings

Constraints on GUP and gravity parameters from Bose-Einstein condensate

More realistic bounds from liquid helium properties

Seismic wave method improves gravity constraints by an order of magnitude

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 $-10^{-1}\lesssim\bar\beta\lesssim 10^{11} \text{ m}^2$ ($-4\times10^{-1}\lesssim\epsilon\lesssim 4\times 10^{11} \text{ m}^2$), 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.