Holography and brane cosmology in domain wall backgrounds

We. consider a class of domain-wall black hole solutions in dilaton gravity with a Liouville-type dilaton potential. Using the surface counterterm. approach we calculate the stress-energy tensor of quantum field theory QFT) corresponding to the domain-wall black hole in the domain-wall-QFT correspondence. A brane universe is investigated in the domain-wall black hole background. When the tension term of the brane is equal to the surface counterterm, we find that the equation of motion of the brane can be mapped to the standard form of Friedmann-Robertson-Walker equations, but with a varying gravitational constant on the brane. A Cardy-Verlinde-like formula is found, which relates the entropy density of the QFT to its energy density. At the moment when the brane crosses the black hole horizon of the back.-round, the Cardy-Verlinde-like formula coincides with the Friedmann equation of the brane universe, and the Hubble entropy bound is saturated by the entropy of domain-wall black holes.