Stability analysis of multiple scalar field cosmologies with matter

Abstract

We investigate the dynamics of a class of Robertson-Walker spacetimes containing multiple scalar fields and ordinary barotropic matter. The potentials for the scalar fields are assumed to be of an exponential form that are multiplicatively coupled. In this case the effective scalar field potential for the m scalar fields j, (1 j m), has the form Veff = j = 1m V0ekjj. We show that the power-law inflationary solution is the local attractor if j = 1m kj2 < 2. In particular, in the case of two scalar fields, we show that the power-law inflationary solution is indeed the global attractor and hence we make the argument that the power-law inflationary solution is also the global attractor in the m scalar field case. If j = 1m kj2 > 2 then we further argue that the curvature scaling solution is the global attractor for the open or negatively curved models. If j = 1m kj2 > 2 then we show that the global attractor for the flat or zero-curvature models is either a power-law solution, a matter scaling solution, or a massless scalar field solution.