A New Method of Generating Exact Inflationary Solutions

Abstract

The mechanism of the initial inflation of the universe is based on gravitationally coupled scalar fields $ϕ$. Various scenarios are distinguished by the choice of an {\it effective self--interaction potential} $U(ϕ)$ which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Using the Hubble expansion parameter $H$ as a new ``time" coordinate, we can formally derive the {\it general} Robertson--Walker metric for a {\em spatially flat} cosmos. Our new method provides a classification of allowed inflationary potentials and is broad enough to embody all known {\it exact} solutions involving one scalar field as special cases. Moreover, we present new inflationary and deflationary exact solutions and can easily predict the influence of the form of $U(ϕ)$ on density perturbations.