Inflationary equilibrium configurations of scalar-tensor theories of gravity

Abstract

In this paper we investigate the asymptotic dynamics of inflationary cosmological models that are based in scalar-tensor theories of gravity. Our main aim is to explore the global structure of the phase space in the framework of single-field inflation models. For this purpose we make emphasis in the adequate choice of the variables of the phase space. Our results indicate that, although single-field inflation is generic in the sense that the corresponding critical point in the phase space exists for a wide class of potentials, along given phase space orbits -representing potential cosmic histories -the occurrence of the inflationary stage is rather dependent on the initial conditions. For the non-minimal coupling model with the φ 2 -potential, we have been able to give a rough estimate of the relative probability for initial conditions leading to slow-roll inflation: 10 −13 % < ∼ RP ≪ 10 −8 %. These bonds are greatly improved in the scalar-tensor models, including the Brans-Dicke theory, where the relative probability RP ∼ 50 %. Hence slow-roll inflation is indeed a natural stage of the cosmic expansion in Brans-Dicke models of inflation. We also clarify an issue with the emergence of the ΛCDM cosmological model from the Brans-Dicke theory. It is confirmed as well that the dynamics of vacuum Brans-Dicke theories with arbitrary potentials are non-chaotic.