Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications

Abstract

We develop a systematic formulation of statistical mechanics on Euclidean Snyder space, where noncommutativity is geometrically encoded in the curvature of momentum space. Adopting a realization independent approach based on momentum-space invariants, we derive modified partition functions and thermodynamic quantities for systems obeying Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics in both non-relativistic and ultrarelativistic regimes. We show that momentum-space curvature induces temperature-dependent corrections that suppress the energy, entropy and energy density with respect to their standard counterparts. We apply these results to early-Universe cosmology, deriving the corresponding corrections to the Friedmann equations driven by the modified energy density of radiation. Using Big Bang Nucleosynthesis as a precision probe, we derive bounds on the Snyder deformation parameter and, via a phenomenological mapping, on the Generalized Uncerainty Principle (GUP) parameter, providing one of the most stringent cosmological and astrophysical constraints currently available. Our analysis demonstrates that high-energy cosmological processes provide a predictive arena for testing momentum-space curvature and noncommutative geometry effects.

13 pages, 1 figure

References in corpus (52)

• String Theory and Noncommutative Geometry
• Thermodynamics of Spacetime: The Einstein Equation of State
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Discreteness of area and volume in quantum gravity
• The quantum structure of spacetime at the Planck scale and quantum fields
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Thermodynamical Aspects of Gravity: New insights
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• Minimal Length Scale Scenarios for Quantum Gravity
• Gravity and the Thermodynamics of Horizons
• Gauge Theory on Noncommutative Spaces
• The algebraic structure of the generalized uncertainty principle
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• Inflation and de Sitter Thermodynamics
• Gravitational tests of the Generalized Uncertainty Principle
• Modified Friedmann Equations from Tsallis Entropy
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
• Modified cosmology through spacetime thermodynamics and Barrow horizon entropy
• Generalized Uncertainty Principle and Corpuscular Gravity
• Some Aspects of Minimal Length Quantum Mechanics
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Constraining f(T) teleparallel gravity by Big Bang Nucleosynthesis
• Constraining non-commutative space-time from GW150914
• Constraining the tidal charge of brane black holes using their shadows
• Relativistic deformed kinematics from momentum space geometry
• Minimal Length, Friedmann Equations and Maximum Density
• Snyder space revisited
• Baryon Asymmetry from the Generalized Uncertainty Principle
• High temperature dimensional reduction in Snyder space
• Particle Dynamics on Snyder space
• Heuristic derivation of Casimir effect in minimal length theories
• Constraints on NonCommutative Spectral Action from Gravity Probe B and Torsion Balance Experiments
• Cosmological constraints on the Generalized Uncertainty Principle from modified Friedmann equations
• Primordial Big Bang Nucleosynthesis and Generalized Uncertainty Principle
• Constraints on massive gravity theory from big bang nucleosynthesis
• The Area Quantum and Snyder Space
• Dark Energy within the Generalized Uncertainty Principle in Light of DESI DR2
• Fermi equation of state with finite temperature corrections in quantum space-times approach: Snyder model vs GUP case
• Generalized Uncertainty Principle mimicking dynamical Dark Energy: matter perturbations and gravitational wave data analysis
• Constraining Snyder and GUP models with low-mass stars
• Multi-Dimensional Cosmology and GUP
• Noncommutative spaces and covariant formulation of statistical mechanics
• Classical electrodynamics on Snyder space
• Early universe thermostatistics in curved momentum spaces
• Covariant dynamics on the momentum space
• Covariant dynamics on the energy-momentum space: scalar field theory