Self-gravitational corrections to the Cardy-Verlinde formula and the FRW brane cosmology in SdS5 bulk

The semiclassical corrections to the Cardy-Verlinde entropy of a five-dimensional Schwarzschild de-Sitter black hole (SdS(5)) are explicitly evaluated. These corrections are considered within the context of KKW analysis and arise as a result of the selfgravitation effect. In addition, a four-dimensional spacelike brane is considered as the boundary of the SdS(5) bulk background. It is already known that the induced geometry of the brane is exactly given by that of a radiation-dominated FRW universe. By exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of SdS(5) bulk black hole as the source for stiff matter. Furthermore, we rewrite the Friedmann-like equation in such a way that it represents the conservation equation of energy of a point particle moving in a one-dimensional effective potential. The self-gravitational corrections to the effective potential and, consequently, to the point particle's motion are obtained. A short analysis on the asymptotic behavior of the four-dimensional brane is presented.