Hyperbolic inflationary model with nonzero curvature

Abstract

We consider a cosmological model consisting of two scalar fields defined in the hyperbolic plane known as hyperbolic inflation. For the background space we consider a homogeneous and isotropic spacetime with nonzero curvature. We study the asymptotic behaviour of the dynamics and we search for attractors in the expanding regime. We prove that the hyperobolic inflation period is an unstable solution and there are not future attractors which can solve the flatness problem and describes acceleration