Exact inflationary solution on the brane

Abstract

We study the evolution of universe with a single scalar field of constant potential minimally coupled to gravity in the brane world cosmology.We find an exact inflationary solution which is not in slow roll.We discuss the limiting cases of the solution.We show that at late times the solution is asymptotic to the de Sitter solution independently of the brane tension. For t → 0 the solution leads to singularity but the nature of the approach to singularity depends upon the brane tension.