The phase-space view of inflation II: fourth-order models - Capozziello, Salvatore; Occhionero, Franco; Amendola, Luca (International journal of modern physics, 1992)
The phase space portrait of the cosmological models deduced from fourth-order gravity theories is discussed with the analytical and numerical methods of our previous paper. A comparison is carried out between models inferred from Lagrangian densities containing powers higher than two in the Ricci scalar of curvature, and the Starobinsky model. Some peculiar structures, such as attractors and singular points, emerging neatly from both theories, have a close physical affinity, in addition to the mathematical one. Trajectories of interest in both scenarios are those undergoing an inflationary expansion and then reaching a Friedmannian asymptotic stable phase. These features are moreover discussed through a potential U(R) in RN-models. Three kinds of potential regions are recognized. They are the allowed regions (a-regions), in which trajectories can reach the Friedmannian phase after possibly undergoing an inflationary period, the disconnected regions (d-regions), in which trajectories, although physical, never reach the Friedmannian stage and the forbidden regions (f-regions), in which there are no physical solutions. A general survey of the global phase space for Starobinsky and RN-models is given via Poincaré projections of suitable variables. a-, d-, and f-regions are represented.
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