Abstract
In this brief note we discuss geodesic flows that correspond to cosmological solutions in higher-dimensional supergravity. On the one hand, we explain that S-brane solutions are in one-to-one correspondence with geodesic curves on the moduli space through dimensional reduction over the brane worldvolume. On the other hand, reduction over the transversal space gives rise to a scalar potential for the moduli and the geodesic motion is deformed. Nonetheless, in most cases, the scalar flow becomes geodesic asymptotically in which case the solution is described by a multi-field scaling cosmology.
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