Dynamics of coset dimensional reduction

The evolution of multiple scalar fields in cosmology has been much studied, particularly when the potential is formed from a series of exponentials. For a certain subclass of such systems it is possible to get ''assisted'' behavior, where the presence of multiple terms in the potential effectively makes it shallower than the individual terms indicate. It is also known that when compactifying on coset spaces one can achieve a consistent truncation to an effective theory which contains many exponential terms; however, if there are too many exponentials then exact scaling solutions do not exist. In this paper we study the potentials arising from such compactifications of eleven-dimensional supergravity and analyze the regions of parameter space which could lead to scaling behavior.