On Inflationary cosmological models

The most common mechanisms leading to in ation are based on models of gravity minimally coupled to a scalar field rolling on a suitable potential V. We discuss such a model defined by the action I = ∫√-g p [R -2 (ϕ)2 )] d4x, in order to find exact general isotropic and homogeneous cosmological solutions displaying an in ationary behavior at early times and a power-law expansion at late times. We also study the effect of the inclusion of matter (in the form of a perfect uid): in this case, we do not find exact solutions because of the non-integrability of the field equations, but we can investigate their global properties (and hence their stability) by means of methods of the theory of dynamical systems.