Dualities versus singularities

We show that a subgroup of the modular group of M-theory compactified on a ten torus, implies the Lorentzian structure of the moduli space, that is us ually associated with naive discussions of quantum cosmology based on the l ow energy Einstein action. This structure implies a natural division of the asymptotic domains of the moduli space into regions which can/cannot be ma pped to Type II string theory or 11D Supergravity (SUGRA) with large radii. We call these the safe and unsafe domains. The safe domain is the interior of the future light cone in the moduli space while the unsafe domain conta ins the spacelike region and the past light cone. Within the safe domain, a pparent cosmological singularities can be resolved by duality transformatio ns and we briefly provide a physical picture of how this occurs. The unsafe domains represent true singularities where all field theoretic description of the physics breaks down. They violate the holographic principle. We arg ue that this structure provides a natural arrow of time for cosmology. All of the Kasner solutions, of the compactified SUGRA theory interpolate betwe en the past and future light cones of the moduli space. We describe tentati ve generalizations of this analysis to moduli spaces with less SUSY.