Unified dark energy from Chiral-Quintom model with a mixed potential in Friedmann--Lemaître--Robertson--Walker cosmology

For a spatially Friedmann-Lemaître-Robertson-Walker cosmology, we propose a multi-scalar field gravitational model. Specifically, we consider a two-scalar field cosmological model in which the kinetic components of the scalar fields establish a two-dimensional sphere of Lorentzian signature. For our Chiral-Quintom model we choose a mixed potential term $V(\phi ,\psi )=V_0{e}^{\lambda \phi }+U_0{e}^{\kappa \phi }{\psi }^{\frac{1}{\sigma }}$ and we investigate the asymptotic limits of the cosmological parameters. This model for $U_0=0$, provides a generalization of the hyperbolic inflation where the equation of the state parameter can cross the phantom divide line. When $U_0\mathrm{\ne }0$ we observe that this cosmological model exhibits asymptotic solutions that encompass accelerated universes, big rip singularities, and dust-like solutions. Hence, this multi-scalar field model it can be regarded as as a dark energy unify model which describes a variety of asymptotic cosmological scenarios.