Statistical Fluctuations as Primordial Correlators in the CMB: Finite Chemical Potential Thermodynamics
Abstract
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 𝒫S(k)∝ k3, with niso=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 𝒫ζX(k⋆)=2.10×10−9 and ns(k⋆)=0.9649, stays within 0.30% of the fitted power law over 0.002≤ k/k⋆≤4, and predicts weak negative running and small positive intrinsic non-Gaussianity from higher-order cumulants, fNL(k⋆)≃0.106 and gNL(k⋆)≃0.0158. With a two-helicity vacuum tensor spectrum, the tensor-to-scalar ratio is rt/s(k⋆)=1.82×10−4. 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.
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BibTeX
@misc{ghoshal2026statistical,
title = {{Statistical Fluctuations as Primordial Correlators in the CMB: Finite Chemical Potential Thermodynamics}},
author = {Anish Ghoshal and Anupam Mazumdar and Bartłomiej Sikorski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24998},
eprint = {2609.24998},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24998},
}
RIS
TY - UNPB
TI - Statistical Fluctuations as Primordial Correlators in the CMB: Finite Chemical Potential Thermodynamics
AU - Anish Ghoshal
AU - Anupam Mazumdar
AU - Bartłomiej Sikorski
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24998
UR - https://arxiv.org/abs/2609.24998
AB - 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 𝒫_S(k)∝ k^3, with n_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 𝒫_ζ_X(k_⋆)=2.10×10^−9 and n_s(k_⋆)=0.9649, stays within 0.30% of the fitted power law over 0.002≤ k/k_⋆≤4, and predicts weak negative running and small positive intrinsic non-Gaussianity from higher-order cumulants, f_NL(k_⋆)≃0.106 and g_NL(k_⋆)≃0.0158. With a two-helicity vacuum tensor spectrum, the tensor-to-scalar ratio is r_t/s(k_⋆)=1.82×10^−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.
ER -