Abstract
For various applications in cosmology and for studying the thermal history of the Universe and its particle content, the bosonic and fermionic distributions, referred to as Bose–Einstein and Fermi–Dirac distributions are needed.
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More precisely we have to replace the energy E(p) in the expression for \(U_\text {b}(p,T)\) by \(E(p) - \mu \), where \(\mu \) is referred to as a chemical potential. Convergence of the integral of (83.1) then requires that \(|\mu | \le m\text {c}^2\). The presence of the chemical potential arises in concordance with specific conservation laws. With the violation of many conservations laws as predicted by GUTs, one may set these chemical potentials equal to zero, which we will do this with no loss of generality. Technically, it denotes the change in energy by one particle given that its entropy and underlying volume remain fixed.
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Manoukian, E.B. (2020). Statistical Distributions. In: 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand. Springer, Cham. https://doi.org/10.1007/978-3-030-51081-7_83
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DOI: https://doi.org/10.1007/978-3-030-51081-7_83
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