Five-dimensional bulk with a time-dependent warp factor and its consequences on brane cosmology

In this paper, we have considered a 5-dimensional warped product space-time with a timedependent warp factor. The time-dependent warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe. We then proceed to determine the nature of modifications produced in the bulk geometry as well as the consequences on the corresponding braneworld. The five-dimensional field equations are constructed. For the bulk metric chosen, the Weyl tensor is found to vanish under a certain condition, thereby satisfying the conditions of a constant curvature bulk. Consequently we have constructed the solutions to the field equations for such a bulk and have studied its physical properties. The braneworld is described by a flat FRW-type metric in the ordinary spatial dimension. It is found that the the effective cosmological constant for the induced matter is a variable quantity monitored by the time-dependent warp factor and is associated with the bending of the braneworlds. The universe is initially decelerated, but subsequently makes a transition to an accelerated phase at later times, when its dynamics is dominated by the dynamical dark energy component. For a particular choice of the warp factor, it has been found that the universe is represented by a model of dark energy with the age of the universe as the measure of length, driving the universe to a state of accelerated expansion at later times.