Heterotic M-Theory Cosmology in Four and Five Dimensions
  We study rolling radii solutions in the context of the four- and five-dimensional effective actions of heterotic M-theory. For the standard four-dimensional solutions with varying dilaton and T-modulus, we find approximate five-dimensional counterparts. These are new, generically non-separating solutions corresponding to a pair of five-dimensional domain walls evolving in time. Loop corrections in the four-dimensional theory are described by certain excitations of fields in the fifth dimension. We point out that the two exact separable solutions previously discovered are precisely the special cases for which the loop corrections are time-independent. Generically, loop corrections vary with time. Moreover, for a subset of solutions they increase in time, evolving into complicated, non-separating solutions. In this paper we compute these solutions to leading, non-trivial order. Using the equations for the induced brane metric, we present a general argument showing that the accelerating backgrounds of this type cannot evolve smoothly into decelerating backgrounds. 
Matthias Braendle, Andre Lukas and Burt A. Ovrut