  In this work we would like to address the problem of the effect of bulk
matter on the brane cosmological evolution in a general way. We assume that the
spatial part of the brane metric is not maximally symmetric, therefore
spatially inhomogeneous. However we retain the conformal flatness property of
the standard cosmological model (FRW) i.e. the Weyl tensor of the induced 4D
geometry is zero. We refer to it as Spatially Inhomogeneous Irrotational (SII)
brane. It is shown that the model can be regarded as the 5D generalization of
the SII spacetimes found recently [1].
