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 \(R<\frac{1}{H}\).

中文翻译：

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D界和Bekenstein界被黑暗能量宇宙场包围的McVittie解

根据施加在被暗能量包围的McVittie解上的熵假说，研究了暗能量的宇宙学候选场，其典型，幻影和宇宙常数。我们将此假设证明为稀体系的“ D界-Bekenstein界识别”，并以此为准则来确定哪个暗能量候选者可以满足稀McVittie解的这一准则。事实证明，只有宇宙学常数才能成功通过该标准，而典型和幻像场却失败了，因为该特定黑洞解决方案的无能暗能量场。此外，假设该黑洞具有饱和熵，则熵面积定律和全息原理可以对半径R施加两个约束宇宙视野。第一个表明哈勃半径是离散的，因此对于黑洞质量\（m_ {0} \）的任意值，R的值最多可以确定为整数。后者表明，当黑洞浸没在宇宙学背景中时，宇宙视界的半径被约束为\（R <\ frac {1} {H} \）。