Brane–World Inflation and the Transition to Standard Cosmology

In the context of a five–dimensional brane–world model motivated from heterotic M–theory, we develop a framework for potential–driven brane–world inflation. Specifically this involves a classification of the various background solutions of (A)dS5 type, an analysis of five–dimensional slow–roll conditions and a study of how a transition to the flat vacuum state can be realized. It is shown that solutions with bulk potential and both bane potentials positive exist but are always non–separating and have a non–static orbifold. It turns out that, for this class of backgrounds, a transition to the flat vacuum state during inflation is effectively prevented by the rapidly expanding orbifold. We demonstrate that such a transition can be realized for solutions where one boundary potential is negative. For this case, we present two concrete inflationary models which exhibit the transition explicitly.