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Abstract
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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 m0, 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 < H1 .
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