SINGULAR SCALAR FIELD COSMOLOGIES WITH ENERGY DENSITY DECAYING AS T(-2)

In search of non-inflationary cosmological models that do not suffer f rom the horizon and the entropy problems of the standard hot big-bang model, we present two exact cosmological solutions to Einstein's equat ions based on a homogeneous scaler field with an exponential potential . The curvature constant k is -1 and 0 in these solutions. The model u niverse of these solutions is singular, causally connected, entropy-co nserving and devoid of matter. We extend these solutions to the more r ealistic case of a universe in which radiation and nonrelativistic mat ter are created through the decay of the homogeneous scalar field. The energy density of the scalar held as well as those of the radiation a nd non-relativistic matter vary with t(-2). The initial entropy of the universe is zero and created as the scalar field decays into radiatio n. The t(-2) variation of the energy densities guarantees a successful cosmic helium synthesis which is essentially indistinguishable from t hat in the standard hot big-bang model. We discuss other aspects of th ese models and argue that they are viable singular models, free of som e of the problems of the standard model.