In this work, we study a Friedmann–Robertson–Walker (FRW) universe derived from a modified entropy–area relationship. By applying the first law of thermodynamics to the so-called apparent horizon and a modified entropy–area relationship, we obtain a modified Friedmann equation. Solving this model for a perfect fluid with vanishing cosmological constant, we find that for early times, the scale factor is the same as that of an FRW universe. In the late-time regime, although the cosmological constant is zero, the asymptotic behavior of the scale factor is exponential, and therefore, we can identify an effective cosmological constant. The origin of the effective cosmological constant can be traced to the modifications of the entropy–area relation.

中文翻译：

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引力熵公式的有效宇宙学常数

在这项工作中，我们研究了从修正的熵-面积关系派生的 Friedmann-Robertson-Walker (FRW) 宇宙。通过将热力学第一定律应用于所谓的视视界和修正的熵-面积关系，我们得到了修正的弗里德曼方程。求解这个模型以获得具有消失的宇宙常数的完美流体，我们发现在早期，比例因子与 FRW 宇宙的比例因子相同。在后期状态下，虽然宇宙常数为零，但比例因子的渐近行为是指数的，因此，我们可以确定一个有效的宇宙常数。有效宇宙学常数的起源可以追溯到熵-面积关系的修改。