Entropy and universality of the Cardy-Verlinde formula in a dark energy universe

Abstract

We study the entropy of a FRW universe filled with dark energy (cosmological constant, quintessence or phantom). For general or time-dependent equation of state $p=w\rho$ the entropy is expressed in terms of energy, Casimir energy, and $w$. The correspondent expression reminds one about 2d CFT entropy only for conformal matter. At the same time, the cosmological Cardy-Verlinde formula relating three typical FRW universe entropies remains to be universal for any type of matter. The same conclusions hold in modified gravity which represents gravitational alternative for dark energy and which contains terms growing at low curvature. It is interesting that BHs in modified gravity are more entropic than in Einstein gravity. Finally, some hydrodynamical examples testing new shear viscosity bound, which is expected to be the consequence of the holographic entropy bound, are presented for the early universe in the plasma era and for the Kasner metric. It seems that the Kasner metric provides a counterexample to the new shear viscosity bound.