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In this work we suggest that higher-dimensional modifications to the mattercontent in FRW spacetimes can be obtained not only, as first considered byPonce de Leon, referring to "moving" 4D hypersurfaces non-orthogonal to thetime-dependent extra dimension of an embedding 5D manifold, but also referringto "fixed" 4D hypersurfaces orthogonal to a suitable scalar function whichdefines a static foliation of the 5D manifold and takes the role of the extradimension in a suitable coordinate system. Results obtained in each approachcrucially depend on the method used to identify the 4D metric of our braneuniverse from the 5D metric of the bulk manifold.

Time-dependent extra dimension and higher-dimensional modifications to the matter content in FRW spacetimes