Cosmological Expansion in the Presence of an Extra Dimension

It was recently pointed out that global solutions of Einstein's equations for a 3-brane universe embedded in four spatial dimensions give rise to a Friedmann equation of the form $H\propto \rho$ on the brane, instead of the usual $H\propto \sqrt{\rho }$, which is inconsistent with cosmological observations. We remedy this problem by adding cosmological constants to the brane and the bulk, as in the recent scenario of Randall and Sundrum. Our observation allows for normal expansion during nucleosynthesis, but faster than normal expansion in the very early universe, which could be helpful for electroweak baryogenesis, for example.