Generalized thermodynamic constraints on holographic-principle-based cosmological scenarios

TL;DR

This paper investigates thermodynamic constraints on holographic cosmological models with arbitrary horizon entropy, finding that the second law limits the driving term to values consistent with observed cosmological constants.

Contribution

It extends previous analyses by considering arbitrary horizon entropies, providing universal thermodynamic constraints on holographic cosmological models.

Findings

The second law constrains the driving term's upper limit.

The upper limit aligns with observed cosmological constant values.

Positivity of entropy also bounds the driving term.

Abstract

The holographic principle can lead to cosmological scenarios, i.e., holographic equipartition models. In this model, an extra driving term (corresponding to a time-varying cosmological term) in cosmological equations depends on an associated entropy on the horizon of the universe. The driving term is expected to be constrained by the second law of thermodynamics, as if the cosmological constant problem could be discussed from a thermodynamics viewpoint. In the present study, an arbitrary entropy on the horizon, $S_{H}$, is assumed, extending previous analysis based on particular entropies [Phys. Rev. D 96, 103507 (2017); (arXiv:1707.09101)]. The arbitrary entropy is applied to the holographic equipartition model, in order to universally examine thermodynamic constraints on the driving term in a flat Friedmann--Robertson--Walker universe at late times. The second law of thermodynamics for the holographic equipartition model is found to constrain the upper limit of the driving term, even if the arbitrary entropy is assumed. The upper limit implies that the order of the driving term is likely consistent with the order of the cosmological constant measured by observations. An approximately equivalent upper limit can be obtained from the positivity of $S_{H}$ in the holographic equipartition model.