Cosmological scenario based on the first and second laws of thermodynamics: Thermodynamic constraints on a generalized cosmological model

Abstract

The first and second laws of thermodynamics should lead to a consistent scenario for discussing the cosmological constant problem. In the present study, to establish such a thermodynamic scenario, cosmological equations in a flat Friedmann-Lemaître-Robertson-Walker universe were derived from the first law, using an arbitrary entropy $S_H$ on a cosmological horizon. Then, the cosmological equations were formulated based on a general formulation that includes two extra driving terms, $f_{\Lambda }(t)$ and $h_{\text{B}}(t)$, which are usually used for, e.g., time-varying $\Lambda (t)$ cosmology and bulk viscous cosmology, respectively. In addition, thermodynamic constraints on the two terms are examined using the second law of thermodynamics, extending a previous analysis [Phys. Rev. D 99, 043523 (2019) (arXiv:1810.11138)]. It is found that a deviation $S_{\Delta }$ of $S_H$ from the Bekenstein-Hawking entropy plays important roles in the two terms. The second law should constrain the upper limits of $f_{\Lambda }(t)$ and $h_{\text{B}}(t)$ in our late Universe. The orders of the two terms are likely consistent with the order of the cosmological constant ${\Lambda }_{\text{obs}}$ measured by observations. In particular, when the deviation $S_{\Delta }$ is close to zero, $h_{\text{B}}(t)$ and $f_{\Lambda }(t)$ should reduce to zero and a constant value (consistent with the order of ${\Lambda }_{\text{obs}}$), respectively, as if a consistent and viable scenario could be obtained from thermodynamics.

Final version accepted for publication in EPJC. Several paragraphs and references are revised. [11 pages, 1 figure]

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