D-bound and Bekenstein bound for McVittie solution surrounded by dark energy cosmological fields

TL;DR

This paper investigates the applicability of entropic bounds to McVittie black hole solutions surrounded by dark energy fields, finding that only the cosmological constant satisfies the proposed criteria, and deriving constraints on the cosmological horizon radius.

Contribution

It introduces a D-bound-Bekenstein bound identification for McVittie solutions and assesses which dark energy candidates satisfy this criterion, highlighting the unique viability of the cosmological constant.

Findings

Only the cosmological constant passes the entropic criterion for dilute McVittie solutions.

The Hubble radius is shown to be discrete and determined up to an integer for any black hole mass.

The cosmological horizon radius is constrained to be less than the inverse Hubble parameter.

Abstract

The cosmological candidate fields for dark energy as quintessence, phantom and cosmological constant, are studied in terms of an entropic hypothesis imposed on the McVittie solution surrounded by dark energy. We certify this hypothesis as "$D$-bound-Bekenstein bound identification" for dilute systems and use it as a criterion to determine which candidate of dark energy can satisfy this criterion for a dilute McVittie solution. It turns out that only the cosmological constant can pass this criterion successfully while the quintessence and phantom fields fail, as non-viable dark energy fields for this particular black hole solution. Moreover, assuming this black hole to possess the saturated entropy, the entropy-area law and the holographic principle can put two constraints on the radius $R$ of the cosmological horizon. The first one shows that the Hubble radius is discrete such that for any arbitrary value of the black hole mass $m_{0}$, the value of $R$ is determined up to an integer number. The latter one shows that when a black hole is immersed in a cosmological background, the radius of the cosmological horizon is constrained as $R<\frac{1}{H}$.