Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles

Petr Jizba; Gaetano Lambiase

doi:10.3390/e25111495

paper

Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles

arXiv:2310.19045 · doi:10.3390/e25111495

Abstract

By employing Tsallis' extensive but non-additive $δ$ -entropy, we formulate the first two laws of thermodynamics for gravitating systems. By invoking Carathéodory's principle, we pay particular attention to the integrating factor for the heat one-form. We show that the latter factorizes into the product of thermal and entropic parts, where the entropic part cannot be reduced to a constant, as is the case in conventional thermodynamics, due to the non-additive nature of $S_{δ}$ . The ensuing two laws of thermodynamics imply a Tsallis cosmology, which is then applied to a radiation-dominated universe to address the Big Bang nucleosynthesis and the relic abundance of cold dark matter particles. It is demonstrated that the Tsallis cosmology with the scaling exponent $δ$ $\sim$ $1.499$ (or equivalently, the anomalous dimension $Δ \sim 0.0013$ ) consistently describes both the abundance of cold dark matter particles and the formation of primordial light elements, such as deuterium $^{2} H$ and helium $^{4} H e$ . Salient issues, including the zeroth law of thermodynamics for the $δ$ -entropy and the lithium $^{7} L i$ problem, are also briefly discussed.

arXiv comment21 pages, 4 figures

Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles

Abstract

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