Dynamics of multi-scalar-field cosmological models and assisted inflation

We investigate the dynamical properties of a class of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials. We show that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these asymptotically stable solutions the curvature is not dynamically negligible). Consequently, we find that in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behavior, contrary to what is commonly believed. The early-time and intermediate behavior of the models is also studied. In particular, n-scalar field models are investigated and the structure of the saddle equilibrium points corresponding to inflationary m-field scaling solutions and non-inflationary m-field matter scaling solutions are also studied (where $m<n),$ leading to interesting transient dynamical behavior perhaps associated with new physical scenarios of potential importance.