统计涨落作为宇宙微波背景中的原初关联子：有限化学势热力学
Statistical Fluctuations as Primordial Correlators in the CMB: Finite Chemical Potential Thermodynamics
- University of Sussex（萨塞克斯大学）
- Canadian Institute of Theoretical Astrophysics, University of Toronto（多伦多大学加拿大理论天体物理研究所）
- Faculty of Physics, University of Warsaw（华沙大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究早期宇宙热系统统计涨落能否产生原初宇宙学关联，发现孤立共形等离子体无法实现标度不变谱，但通过准德西特阶段的开放无质量狄拉克费米子系统可生成近似标度不变的红曲率谱，并给出与观测一致的基准预测。
AI中文摘要：
原初宇宙学关联能否起源于早期宇宙热系统的统计涨落？我们将巨正则热力学、随机输运和规范不变的宇宙学扰动联系起来，研究对象为有限化学势下的带电流体。能量-电荷磁化率决定曲率扰动、电荷等曲率扰动及交叉关联的幅度，而输运过程决定每种模式何时离开平衡。对于孤立、绝热且具有守恒电荷-熵比和幂律扩散的共形等离子体，扩散冻结产生普适谱 $\mathcal P_S(k)\propto k^3$，其中 $n_{\rm iso}=4$，而在共形源基中，等时局域平衡曲率-等曲率协方差为零。因此，有限化学势或仅用扩散穿越替代哈勃穿越都不能单独产生近似标度不变性。我们通过一个在受源准德西特阶段的无质量狄拉克费米子开放子系统来规避这一障碍。在该系统中，巨正则能量累积量产生近似标度不变的红曲率谱。基准计算给出 $\mathcal P_{\zeta_X}(k_\star)=2.10\times10^{-9}$ 和 $n_s(k_\star)=0.9649$，在 $0.002\leq k/k_\star\leq4$ 范围内与拟合幂律的偏差保持在 $0.30\\%$ 以内，并预测来自高阶累积量的弱负跑动和小的正固有非高斯性，$f_{\rm NL}(k_\star)\simeq0.106$ 和 $g_{\rm NL}(k_\star)\simeq0.0158$。采用双螺旋真空张量谱时，张标比为 $r_{t/s}(k_\star)=1.82\times10^{-4}$。这揭示了孤立共形热播种的局限性以及克服该局限性所需的开放系统要素。因此，热能量-电荷涨落为现实标量关联提供了可计算的来源，而储层动力学、平衡化及后续曲率-等曲率转移必须来自微观模型。
英文摘要：
Can primordial cosmological correlations originate from statistical fluctuations of an early-universe thermal system? We connect grand-canonical thermodynamics, stochastic transport, and gauge-invariant cosmological perturbations for a charged fluid at finite chemical potential. Energy-charge susceptibilities determine curvature, charge-isocurvature, and cross-correlation amplitudes, while transport sets when each mode leaves equilibrium. For an isolated, adiabatic conformal plasma with conserved charge-to-entropy ratio and power-law diffusion, diffusive freeze-out yields the universal spectrum $\mathcal P_S(k)\propto k^3$, with $n_{\rm iso}=4$, while equal-time local-equilibrium curvature-isocurvature covariance vanishes in the conformal source basis. Thus neither finite chemical potential nor replacing Hubble crossing by diffusion crossing alone yields approximate scale invariance. We evade this obstruction with an open subsystem of massless Dirac fermions during a sourced quasi-de Sitter phase. There, grand-canonical energy cumulants generate a nearly scale-invariant red curvature spectrum. A benchmark gives $\mathcal P_{ζ_X}(k_\star)=2.10\times10^{-9}$ and $n_s(k_\star)=0.9649$, stays within $0.30%$ of the fitted power law over $0.002\leq k/k_\star\leq4$, and predicts weak negative running and small positive intrinsic non-Gaussianity from higher-order cumulants, $f_{\rm NL}(k_\star)\simeq0.106$ and $g_{\rm NL}(k_\star)\simeq0.0158$. With a two-helicity vacuum tensor spectrum, the tensor-to-scalar ratio is $r_{t/s}(k_\star)=1.82\times10^{-4}$. This isolates the limitation of isolated conformal thermal seeding and the open-system ingredient needed to overcome it. Thermal energy-charge fluctuations thus provide a calculable source of realistic scalar correlations, while reservoir dynamics, equilibration, and later curvature-isocurvature transfer must come from a microscopic model.
