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

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-Lema\^{i}tre-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 $h_{\textrm{B}}(t)$, 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 $h_{\textrm{B}}(t)$ in our late Universe.

The orders of the two terms are likely consistent with the order of the cosmological constant $\Lambda_{\textrm{obs}}$ measured by observations.

In particular, when the deviation $S_{\Delta}$ is close to zero, $h_{\textrm{B}}(t)$ and $f_{\Lambda}(t)$ should reduce to zero and a constant value (consistent with the order of $\Lambda_{\textrm{obs}}$), respectively, as if a consistent and viable scenario could be obtained from thermodynamics.

;Comment: References are added and updated.

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