Cosmological 3-brane solutions

We analyze cosmological equations in the brane world scenario with one extr a space-like dimension. We demonstrate that the cosmological equations can be reduced to the usual 4D Friedmann type if the bulk energy-momentum tenso r is different from zero. We then generalize these equations to the case of a brane of finite thickness. We also demonstrate that when the bulk energy -momentum tensor is different from zero, the extra space-like dimension can be compactified with a single brane and show that the stability of the rad ius of compactification implies standard cosmology and vice versa. For a br ane of finite thickness, we provide a solution such that the 4D Planck scal e is related to the fundamental scale by the thickness of the brane. In thi s case, compactification of the extra dimension is unnecessary. (C) 1999 Pu blished by Elsevier Science B.V. All rights reserved.