Cosmological expansion in the Randall-Sundrum brane world scenario - art. no. 044039

The cosmology of the Randall-Sundrum scenario for a positive tension brane in a 5D universe with localized gravity has been studied previously. In the radiation-dominated universe, it was suggested that there are two solution s for the cosmic scale factor a(t): the standard solution a similar to t(1/ 2), and a solution a similar to t(1/4), which is incompatible with standard big bang nucleosynthesis. In this paper, we reconsider expansion of the Un iverse in this scenario. We derive and solve a first order, linear differen tial equation for H-2, the square of the expansion rate of the Universe, as a function of a. The differences between our equation for H-2 and the rela tionship found in standard cosmology are (i) there is a term proportional t o density squared (a fact already known), which is small when the density i s small compared to the brane tension, and (ii) there is a contribution whi ch acts like a relativistic fluid. We show that this second contribution is due to gravitational degrees of freedom in the bulk. Thus, we find that th ere need not be any conflict between cosmology of the Randall-Sundrum scena rio and the standard model of cosmology. We discuss how reheating at the en d of inflation leads to the correct relationship between matter density and expansion rate, H-2-->8 pi G rho(m)/3, and the conditions that must be met for the expansion rate of the universe to be close to its standard model v alue around the epoch of cosmological nucleosynthesis.