Exact Conformal Scalar Field Cosmologies

TL;DR

This paper derives new exact solutions in Einstein's gravity with a conformal scalar field, revealing diverse cosmological behaviors including inflation, coasting, and bouncing models, expanding understanding of scalar field cosmologies.

Contribution

It extends a solution-generating technique to find new exact cosmological solutions with conformal scalar fields in Einstein's gravity.

Findings

Solutions exhibit power-law inflationary behavior.

Some models approach coasting universe dynamics.

Bouncing models avoiding initial singularity are presented.

Abstract

New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a Friedmann-Robertson-Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour $S(t)\sim t^p$ with $p>1$, while another class exhibits a late time approach to the $S(t)\sim t$ behaviour of the coasting models. Bouncing models which avoid an initial singularity are also obtained. A general discussion of the asymptotic behaviour and of the possibility of occurrence of inflation is provided.