Inflationary models with exponential potentials

Abstract

In this paper we consider cosmological models containing a self-interacting scalar field possessing a potential of the form V( φ) = Λ exp(− λφ). We investigate the inflationary nature of the model in an ( N + 1)-dimensional Friedman space-time as well as in some (3 + 1)-dimensional anisotropic cosmological models. We determine the conditions under which power-law inflation occurs by a detailed stability analysis which determines all possible asymptotic behaviour. We also present some new exact solutions which exhibit the transition to power-law inflation. We determine the range of evolutionary behaviours in each case for all λ ⩾ 0 and find the range of λ values for which power-law inflation occurs. We also discuss how potentials of the exponential type may arise in realistic models of the early universe.