Title: Inhomogeneous brane models

Abstract: Intrinsic Conformal Symmetries have emerged as a tool for developing viable and physically coherent models, particularly in scenarios incorporating a negative cosmological constant. This study demonstrates that when the bulk geometry accommodates a set of $10$ Intrinsic Conformal Symmetries, which operate on three-dimensional hypersurfaces (be they spacelike or timelike), it leads to the existence of two distinct families of five-dimensional spacetimes. These spacetimes represent the general solutions to the bulk field equations. An aspect of these models is the composition of their energy-momentum tensor, which includes two key components: a negative cosmological constant and a parallel pressure $p_{\parallel}$ aligned with the extra spatial dimension. This framework can be perceived as a $5D$ extension of the recently identified Spatially Inhomogeneous and Irrotational spacetimes. Significantly, these models offer a novel perspective for investigating the impacts of spatial inhomogeneity on the cosmological evolution of the Universe, particularly within the context of the Randall-Sundrum theory. This exploration is essential for deepening our understanding of the role of higher dimensions in cosmological models.