Behavior of Friedmann-Robertson-Walker Cosmological Models in Scalar-Tensor Gravity

TL;DR

This paper investigates the dynamics of Friedmann-Robertson-Walker cosmologies within scalar-tensor gravity, revealing complex behaviors like bifurcations, non-inflationary models, and conditions affecting inflation, challenging traditional inflationary assumptions.

Contribution

It introduces a reduction of the field equations to a two-dimensional dynamical system and analyzes the full solution space, uncovering new qualitative features of scalar-tensor cosmologies.

Findings

Many cosmological behaviors including bifurcations and bouncing universes identified.

Inflation depends on initial scalar field energy, not just curvature and matter.

Exact power-law solutions are recovered for flat space cases.

Abstract

We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory, where a scalar field is coupled to gravity. Matter is modelled by a $\gamma$-law perfect fluid, including false-vacuum energy as a special case. Through a change of variables, we reduce the field equations from fourth order to second order, and they become equivalent to a two-dimensional dynamical system. We then analyze the entire solution space of this dynamical system, and find that many qualitative features of these cosmologies can be gleaned, including standard non-inflationary or extended inflationary expansion, but also including bifurcations of stable or unstable expansion or contraction, noninflationary vacuum-energy dominated models, and several varieties of ``coasting," ``bouncing," ``hesitating," and ``vacillating" universes. It is shown that inflationary dogma, which states that a universe with curvature and dominated by inflationary matter will always approach a corresponding flat-space solution at late times, does not hold in general for the scalar-tensor theory, but rather that the occurence of inflation depends upon the initial energy of the scalar field relative to the expansion rate. In the case of flat space ($k=0$), the dynamical system formalism generates some previously known exact power-law solutions.