Cosmological models arising from generalized scalar field potentials

Abstract

We find exact solutions for isotropic cosmological models containing a self-interacting scalar field possessing an interaction potential of a general class. In particular, we consider the combination of exponential potentials arising from a perturbation expansion in superstring theories. We also consider a general class of potentials that give rise to power-law and polynomial chaotic inflation, as well as the intermediate inflationary models. We compute the scalar and tensor perturbations produced in those models and use the exact solutions obtained to examine the consistency of the first-order slow-roll expansion.