Hyperbolic inflationary model with nonzero curvature

TL;DR

This paper explores a hyperbolic inflationary cosmological model with nonzero curvature, identifying stable inflationary solutions and attractors that address the flatness problem and describe accelerated expansion.

Contribution

It introduces a hyperbolic inflation model with nonzero curvature and analyzes its stability, attractors, and dynamical behaviors in both expanding and contracting regimes.

Findings

Two stable hyperbolic inflationary stages identified.

Solutions can address the flatness problem and describe acceleration.

Discovery of a Milne-like attractor for open models.

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 solutions and we search for attractors in the expanding regime. We prove that two hyperbolic inflationary stages are stable solutions that can solve the flatness problem and describe acceleration for both open and closed models, and additionally we obtain a Milne-like attractor solution for the open model. We also investigate the contracting branch obtaining mirror solutions with the opposite dynamical behaviours.