Corrected entropy-area relation and modified Friedmann equations
Corrected entropy-area relation and modified Friedmann equations
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修正的熵面积关系和修正的弗里德曼方程
DOI：
10.1088/1126-6708/2008/08/090
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发表时间：
2008-08-01
影响因子：
5.4
通讯作者：
Hu, Ya-Peng
中科院分区：
文献类型：
--
作者：
Cai, Rong-Gen;Cao, Li-Ming;Hu, Ya-Peng
将克劳修斯关系应用于任意空间曲率的FRW宇宙的视界，并假定视界温度T=1/(2 pi(R)/tideA)，以及量子修正的熵-面积关系S=A/4G+allna/4G，其中tideA和A上的(R)分别是视界半径和视界面积，α是一个无量纲常数，我们得到了修正的Friedmann方程，它不包含反弹解.另一方面，环路量子宇宙学得到了修正的Friedmann方程H-2=8pG/3Rho(1-Rho/Rho(Crit))。我们得到了由修正的Friedmann方程描述的FRW宇宙视界的熵表达式。在大视界范围内，得到的熵表达式给出了上述修正后的熵-面积关系，但对数项中的前因子α为正，这似乎与文献中有关量子几何导致对黑洞熵面积公式的负贡献的结果不一致。
Applying Clausius relation, delta Q = TdS, to apparent horizon of a FRW universe with any spatial curvature, and assuming that the apparent horizon has temperature T = 1/(2 pi(r) over tildeA), and a quantum corrected entropy-area relation, S = A/4G + alpha lnA/4G, where (r) over tildeA and A are the apparent horizon radius and area, respectively, and alpha is a dimensionless constant, we derive modified Friedmann equations, which does not contain a bounce solution. On the other hand, loop quantum cosmology leads to a modified Friedmann equation H-2 = 8 pi G/3 rho(1-rho/rho(crit)). We obtain an entropy expression of apparent horizon of FRW universe described by the modified Friedmann equation. In the limit of large horizon area, resulting entropy expression gives the above corrected entropy-area relation, however, the prefactor alpha in the logarithmic term is positive, which seems not consistent with most of results in the literature that quantum geometry leads to a negative contribution to the area formula of black hole entropy.