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Global stability analysis for scalar‐tensor models
Author(s) -
Amendola L.,
Occhionero F.
Publication year - 1990
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113110307
Subject(s) - physics , quartic function , phase space , parameter space , scalar field , instability , scalar (mathematics) , attractor , inflaton , coupling constant , quadratic equation , mathematical physics , curvature , singularity , classical mechanics , coupling (piping) , theoretical physics , inflation (cosmology) , quantum mechanics , mathematical analysis , mathematics , geometry , mechanical engineering , pure mathematics , engineering
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 (ϕ 2 n ) 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.