The finite temperature effect is examined in Randall-Sundrum brane-world scenario with inclusion of the matter fields on the brane. At zero temperature it is found that the theory on the brane is conformally invariant, which guarantees AdS/CFT. At 4d effective action we derived a temperature-dependent nonvanishing cosmological constant at the flat spacetime limit of brane worldvolume. At the cosmological temperature 3K the cosmological constant is roughly (0.0004eV ) 4 which is within the upper bound of the recent experimental value (0.01eV ) 4 *

A new mechanism which leads to a linearized massless graviton localized on the brane is found in the AdS/CFT setting, i.e. in a single copy of AdS 5 spacetime with a singular brane on the boundary, within the Randall-Sundrum brane-world scenario. With an help of a recent development in path-integral techniques, a one-parameter family of propagators for linearized gravity is obtained analytically, in which a parameter ξ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition (ξ = 0) the graviton localized on the brane can be massless via coupling constant renormalization. Our result supports a conjecture that the usual Randall-Sundrum scenario is a regularized version of a certain underlying theory. *

The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A criterion is derived for the occurrence of a first-order type transition, and the related phase diagram for scalar and vector fields is obtained. For scalar fields both the first and second order transitions can occur depending on the shape of the potential barrier. For a vector field, here that of an O(3) nonlinear $\sigma$-model, the transition is seen to be only of the first order.Comment: 15 pages, 3 figure