GLOBAL STABILITY ANALYSIS FOR SCALAR-TENSOR MODELS

The phase space of a cosmological model with a scalar field coupled to curvature is discussed in detail for any value of the coupling constant ξ and any power law (ϕ2n) potential. The results obtained generalize previous studies with minimal coupling (ξ = 0) and quadratic or quartic potentials to the entire parameter space (ξ, n). In many cases one finds global attractors and inflationary trajectories, with or without the correct Friedmannian limit. If the coupling constant is positive, a forbidden region cuts out a large part of the phase space, while, if it is negative, escaping regions may occur. Semi‐classical instability of vacuum states and singularity‐free trajectories are also discussed. Copyright © 1990 WILEY‐VCH Verlag GmbH & Co. KGaA