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.

arXiv comment9 pages, 3 figures

References in corpus (54)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Dynamics of dark energy
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• A Generalized Uncertainty Principle in Quantum Gravity
• Discreteness of Space from the Generalized Uncertainty Principle
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Prospects for probing the dark energy via supernova distance measurements
• Eddington's theory of gravity and its progeny
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem
• Born-Infeld inspired modifications of gravity
• Generalized Uncertainty Principle: Approaches and Applications
• Accelerated Cosmological Models in Ricci squared Gravity
• Compact stars in Eddington inspired gravity
• Linking Tests of Gravity On All Scales: from the Strong-Field Regime to Cosmology
• Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics
• Surface singularities in Eddington-inspired Born-Infeld gravity
• Hydrogen Burning in Low Mass Stars Constrains Alternative Gravity Theories
• Minimal Length in Quantum Gravity, Equivalence Principle and Holographic Entropy Bound
• Testing Gravity Using Dwarf Stars
• Instabilities in Metric-Affine Theories of Gravity
• Universality of Einstein Equations for the Ricci Squared Lagrangians
• Vainshtein regime in Scalar-Tensor gravity: constraints on DHOST theories
• Physics at the surface of a star in Eddington-inspired Born-Infeld gravity
• Minimum main sequence mass in quadratic Palatini $f(\mathcal{R})$ gravity
• Statistical mechanics and thermodynamic limit of self-gravitating fermions in D dimensions
• Palatini $f(R)$ gravity in the solar system: post-Newtonian equations of motion and complete PPN parameters
• Equilibrium and stability of relativistic stars in extended theories of gravity
• On stability of a neutron star system in Palatini gravity
• Stability criterion for white dwarfs in Palatini $f(R)$ gravity
• Extended GUP formulation and the role of momentum cut-off
• Generalized Uncertainty Principle Removes The Chandrasekhar Limit
• Modified commutators are not sufficient to determine a quantum gravity minimal length scale
• Early evolutionary tracks of low-mass stellar objects in modified gravity
• Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
• Fermi gas and modified gravity
• Effect of Generalized Uncertainty Principle on Main-Sequence Stars and White Dwarfs
• Lithium abundance is a gravitational model dependent quantity
• Metric-affine effects in crystallization processes of white dwarfs
• Higher mass limits of neutron stars from the equation of states in curved spacetime
• A Subtle Aspect of Minimal Lengths in the Generalized Uncertainty Principle
• Equation of states in the curved spacetime of spherical degenerate stars
• Existence of Chandrasekhar's limit in GUP white dwarfs
• New higher-order generalized uncertainty principle: Applications
• Fermi equation of state with finite temperature corrections in quantum space-times approach: Snyder model vs GUP case
• Do we need dense matter equation of state in curved spacetime for neutron stars?
• Unveiling Phase Space Modifications: A Clash of Modified Gravity and the Generalized Uncertainty Principle
• Planetary seismology as a test of modified gravity proposals
• Constraining Snyder and GUP models with low-mass stars
• Early evolution of fully convective stars in scalar-tensor gravity
• On the Chandrasekhar Limit in Generalized Uncertainty Principles
• Deformed classical-quantum mechanics transition

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