欧几里得辛格空间的统计力学：与GUP和宇宙学含义的联系
Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications
AI总结：
本文研究了欧几里得辛格空间中的统计力学，推导了修正的配分函数和热力学量，并应用于早期宇宙学，推导了辐射能量密度的修正，从而对GUP参数和辛格变形参数设定了严格的宇宙学约束。
摘要：
我们发展了欧几里得辛格空间上的统计力学系统化表述，其中非交换性在动量空间曲率中几何地编码。采用基于动量空间不变量的独立实现方法，我们推导了遵循麦克斯韦-玻尔兹曼、玻色-爱因斯坦和费米-狄拉克统计的系统在非相对论和超相对论极限下的修正配分函数和热力学量。我们显示动量空间曲率诱导温度依赖的修正，抑制能量、熵和能量密度相对于标准对应物。我们将这些结果应用于早期宇宙学，推导了由修正辐射能量密度驱动的弗里德曼方程的相应修正。利用大爆炸核合成作为精确探测器，我们推导了辛格变形参数的界限，并通过现象学映射推导了广义不确定性原理（GUP）参数的界限，提供了目前最严格的宇宙学和天体物理约束。我们的分析表明，高能宇宙学过程为测试动量空间曲率和非交换几何效应提供了预测性领域。
英文摘要：
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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