The authors construct μ-extensions of iterated integrals and nested sums over multiple alphabets, showing that they map polynomially in μ into the original function space (except for square-root cases) while preserving Hopf algebra structure via the quasi-shuffle product.
Condensate of $\mu$-Bose gas as a model of dark matter
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abstract
Though very popular, Bose-Einstein condensate models of dark matter have some difficulties. Here we propose the so-called $\mu$-Bose gas model ($\mu$-BGM) as a model of dark matter, able to treat weak points. Within $\mu$-BGM, the $\mu$-dependence of thermodynamics arises through the respective $\mu$-calculus (it generalizes usual differential calculus) and enters the partition function, total number of particles, internal energy, etc. We study thermodynamic geometry of the $\mu$-BGM and find singular behavior of (scalar) curvature, confirming Bose-like condensation. The critical temperature of condensation $T^{(\mu)}_c$ for $\mu\neq 0$ is higher than the boson $T_c$. We find other important virtues of $\mu$-thermodynamics versus usual bosons and conclude: the condensate of $\mu$-Bose gas can serve as (an effective) model of galactic-halos dark matter.
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hep-th 1years
2026 1verdicts
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The $\mu$-extension of iterated integrals and nested sums
The authors construct μ-extensions of iterated integrals and nested sums over multiple alphabets, showing that they map polynomially in μ into the original function space (except for square-root cases) while preserving Hopf algebra structure via the quasi-shuffle product.