Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1994-05-07
Ann.Phys.241:128-151,1995
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Slight stylistic changes and some references added. This version to be published in {\sl Annals of Physics}
Scientific paper
10.1006/aphy.1995.1058
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.
Eardley Douglas M.
Kolitch Shawn J.
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