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

Boris Ivetić; Giuseppe Gaetano Luciano

doi:10.1016/j.physletb.2026.140627

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arXiv · 2602.02506

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

Boris Ivetić·Giuseppe Gaetano Luciano

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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.

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Boris Ivetić, Giuseppe Gaetano Luciano. 2026-01-22. Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications. https://doi.org/10.1016/j.physletb.2026.140627

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