Cosmology with positive and negative exponential potentials

We present a phase-plane analysis of cosmologies containing a scalar field phi with an exponential potential V proportional to exp(-lambdakappaphi) where kappa(2) = 8piG and V may be positive or negative. We show that power-law kinetic-potential scaling solutions only exist for sufficiently flat (lambda(2) < 6) positive potentials or steep (lambda(2) > 6) negative potentials. The latter correspond to a class of ever-expanding cosmologies with negative potential. However, we show that these expanding solutions with a negative potential are unstable in the presence of ordinary matter, spatial curvature or anisotropic shear, and generic solutions always recollapse to a singularity. Power-law kinetic-potential scaling solutions are the late-time attractor in a collapsing universe for steep negative potentials(the ekpyrotic scenario) and stable against matter, curvature or shear perturbations. Otherwise kinetic-dominated solutions are the attractor during collapse (the pre-big-bang scenario) and are only marginally stable with respect to anisotropic shear.