Non singular M theory Universe in Loop Quantum Cosmology -- inspired Models

Abstract: We study an M theory universe in the Loop Quantum Cosmology -- inspired models which involve a function, the choice of which leads to a variety of evolutions. The M theory universe is dominated by four stacks of intersecting brane--antibranes and, in general relativity, it becomes effectively four dimensional in future while its seven dimensional internal space reaches a constant size. We analyse the conditions required for non singular evolutions and obtain explicit solutions in the simplified case of a bi--anisotropic universe and a piece--wise linear function for which the evolutions are non singular. One may now ask whether the physics in the Planckian regime can enhance the internal volume to phenomenologically interesting values. In the simplified case considered here, there is no non trivial enhancement. We make some comments on it.