THE PHASE-SPACE VIEW OF INFLATION I: THE NON-MINIMALLY COUPLED SCALAR FIELD

Abstract

The Phase Space portrait of a cosmological model with a scalar field coupled to curvature is discussed in detail, analytically and numerically, for any value of the coupling constant ξ and any power law (ϕ2n) potential. The results, particularly intuitive from the graphical point of view, generalize previous studies on the phase space with minimal coupling (ξ = 0) and quadratic or quartic potentials to the entire parameter space (ξ, n). We find global inflationary attractors, often in analytical form, with or without the correct Friedmannian limit. If the coupling constant is negative, escaping regions may occur, while, if it is positive, a forbidden region cuts out a large part of the phase space. Semiclassical instability of vacuum states and singularity-free trajectories are also discussed.