Scalar field cosmologies and the initial spacetime singularity

The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW spacetime is analysed in detail using a dynamical systems approach which may readily be generalized to more complicated spacetimes. It is shown that for a very large and natural class of models a simple and regular past asymptotic structure exists. More specifically, there exists a family of solutions which is in continuous one-to-one correspondence with the exactly integrable massless scalar field cosmologies, this correspondence being realized by a unique asymptotic approximation. The set of solutions which do not fall into this class has measure zero. The significance of this result to the cosmological initial-value problem is discussed briefly.