Semi-Analytical Analysis of Helium Synthesis in Brane Cosmology

The problem of primordial nucleosynthesis of helium in brane cosmology is studied using a semi-analytical method, where the Fermi-Dirac statistic is ignored. This semi-analytical method agrees with a more complete numerical calculation with a precision of order of 10% or better. The quadratic term for the matter density is the only source considered in the modified Einstein equations predicted by the brane configuration. This hypothesis is justified a posteriori. An agreement between theoretical and observational values for the helium abundance is obtained if the fundamental mass scale in five dimensions is of the order of $M \sim 5\times10^3 GeV$.