Dynamical Systems Treatment of Scalar Field Cosmologies

TL;DR

This paper analyzes scalar field cosmologies using dynamical systems, showing that scalar fields have minimal effects in radiation universes and that inflation depends on initial conditions rather than being a universal attractor.

Contribution

It provides a dynamical systems approach to scalar field cosmologies, clarifying the impact of scalar fields and initial conditions on inflationary behavior.

Findings

Scalar fields have negligible impact in radiation-dominated universes.

Inflation depends on initial scalar field kinetic energy, not just model parameters.

Power-law inflation is not a universal attractor for closed universes.

Abstract

The conformal equivalence of some cosmological models in Brans-Dicke theory to general relativistic cosmologies with a scalar field is discussed. In the case of radiation-dominated universes, it is shown that the presence of the scalar field has a negligible impact upon the evolution of the models in the Einstein frame. It is also shown that power-law inflation in general relativity, which is conformal to ``extended'' power-law inflation in Brans-Dicke theory, is not a unique attractor for expanding closed universes, but rather that the occurence of inflation depends upon the initial kinetic energy of the scalar field.