Corrected entropy-area relation and modified Friedmann equations

By R. Cai, Li-Ming Cao, Yapeng Hu. 2008

243 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6cced38ee4eb23fe810712240eee16a83c090ac2

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In Astronomy and Astrophysics

1. Pedro G. S. Fernandes
2. Yi Wang
3. Shuang Wang
4. Miao Li
5. R. Cai
6. N. Ohta
7. Li-Ming Cao
8. T. Clifton

In Nuclear and High Energy Physics

1. Pedro G. S. Fernandes
2. Yi Wang
3. Shuang Wang
4. R. Cai
5. Miao Li
6. N. Ohta
7. Li-Ming Cao
8. T. Clifton

In Statistical and Nonlinear Physics

1. Pedro G. S. Fernandes
2. N. Ohta
3. R. Cai
4. Li-Ming Cao
5. Miao Li
6. Shuang Wang
7. Yi Wang
8. T. Clifton

Citations in the corpus

• Holographic dark energy (2016, background): “The corrections in general take the following form (see, for example, [413, 414, 415])”
• The 4D Einstein–Gauss–Bonnet theory of gravity: a review (2022, background): “Interestingly, these Friedmann equations have exactly the same form as the ones obtained in holographic cosmology [230, 231], from the generalized uncertainty principle [232], by considering quantum entropic corrections [233], and from gravity with a conformal anomaly [234].”
• Friedmann Equations from Entropic Force (2010, background): “For more references see, for example [9, 10] and references therein.”