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

TL;DR

This paper explores how thermodynamic laws constrain generalized cosmological models with time-varying terms, ensuring their consistency with observed cosmological constants and entropy considerations.

Contribution

It derives cosmological equations from thermodynamics with generalized entropy and examines constraints on model terms using the second law, extending previous analyses.

Findings

Thermodynamic constraints limit the magnitude of model terms.

Deviations in entropy influence the behavior of cosmological functions.

Models are consistent with observed cosmological constant when entropy deviation is minimal.

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-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.