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Models of Gravity in Five-dimensional Warped Product Spactimes

In this paper, we have considered gravity in a 5-dimensional warped product space-time with a time-dependent warp factor, time-dependent extra dimension and a bulk cosmological constant. The braneworld is described by a spatially flat FRW-type metric. The five-dimensional field equations have been constructed and solved for various cases of the warp factor and the extra-dimensional scale factor, starting from very general type of the metric and then reducing down to specific cases. In the low energy regime, a stabilized bulk with constant curvature has been considered, from which the cosmological behavior of the corresponding observed universe has been interpreted. In the high energy regime, the bulk is assumed to be sourced by an ordinary massless scalar field and thereafter the type of the scalar field source and the different scale factors have been investigated.