$\mathcal{N}$-field cosmology in hyperbolic field space: stability and general solutions

Abstract

We study the dynamics of a cosmological model with a perfect fluid and $\mathcal{N}$ fields on a hyperbolic field space interacting via a symmetric potential. We list all late-time solutions, investigate their stability and briefly discuss predictions of the theory. Moreover, for the case of two scalar fields and an exponential potential we prove that the field equations are Liouville integrable and we provide for the first time the general solution for a region of the parameter space.