A New Method of Generating Exact Inflationary Solutions

TL;DR

This paper introduces a novel method for generating exact inflationary solutions in cosmology, classifying potentials and deriving new solutions, with implications for understanding density perturbations.

Contribution

A new approach using the Hubble parameter as a time coordinate to classify and derive exact inflationary solutions with scalar fields.

Findings

Provides a classification scheme for inflationary potentials.

Derives new exact inflationary and deflationary solutions.

Predicts the influence of potential form on density perturbations.

Abstract

The mechanism of the initial inflation of the universe is based on gravitationally coupled scalar fields $\phi$. Various scenarios are distinguished by the choice of an {\it effective self--interaction potential} $U(\phi)$ 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 $U(\phi)$ on density perturbations.