We analyze cosmological equations in the brane world scenario with one extra space-like dimension. We demonstrate that the cosmological equations can be reduced to the usual 4D Friedmann type if the bulk energy-momentum tensor 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 radius of compactification implies standard cosmology and vice versa. For a brane of finite thickness, we provide a solution such that the 4D Planck scale is related to the fundamental scale by the thickness of the brane. In this case, compactification of the extra dimension is unnecessary.
|Original language||English (US)|
|Number of pages||9|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - 1999|
Bibliographical noteFunding Information:
This work was supported in part by the Department of Energy under Grant No. DE-FG-02-94-ER-40823 at the University of Minnesota, and PPARC grant GR/L56565 and INTAS 95-RFBR-567 at Oxford. One of us (I.K.) wants to thank TPI and Department of Physics, University of Minnesota for its hospitality during the summer of 1999 where this work began.