Note on the chemical potential of decoupled matter in the Universe

Abstract

Textbooks on cosmology exhibit a thermodynamic inconsistency for free streaming, decoupled matter. It is connected here to the chemical potential, which deviates from its equilibrium value $\mu =\alpha k_{B}T$, where $\alpha$ is the usual parameter of the Fermi-Dirac or Bose-Einstein distribution function.

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