Dj. Holden et D. Wands, PHASE-PLANE ANALYSIS OF FRIEDMANN-ROBERTSON-WALKER COSMOLOGIES IN BRANS-DICKE GRAVITY, Classical and quantum gravity (Print), 15(10), 1998, pp. 3271-3290
We present an autonomous phase plane describing the evolution of Fried
mann-Robertson-Walker models containing a perfect fluid (with barotrop
ic index gamma) in Brans-Dicke gravity (with Brans-Dicke parameter ome
ga). We find fixed points corresponding to Nariai's power-law solution
s for spatially hat models and curvature-scaling solutions for curved
models. At infinite values of the phase-plane variables we recover O'H
anlon and Tupper's vacuum solutions for spatially flat models and the
Milne universe for negative spatial curvature. We find conditions for
the existence and stability of these critical points and describe the
qualitative evolution in all regions of the (omega, gamma)-parameter s
pace for 0 less than or equal to gamma less than or equal to 2 and ome
ga > - 3/2. We show that the condition for inflation in Brans-Dicke gr
avity is always more restrictive than the general relativistic conditi
on, gamma < 2/3.