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For a spatially Friedmann-Lema\^{\i}tre-Robertson-Walker cosmology, wepropose a multi-scalar field gravitational model. Specifically, we consider atwo-scalar field cosmological model in which the kinetic components of thescalar fields establish a two-dimensional sphere of Lorentzian signature. Forour 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 weinvestigate the asymptotic limits of the cosmological parameters. This modelfor $U_{0}=0$, provides a generalization of the hyperbolic inflation where theequation of the state parameter can cross the phantom divide line. When$U_{0}\neq0$ we observe that this cosmological model exhibits asymptoticsolutions that encompass accelerated universes, big rip singularities, anddust-like solutions. Hence, this multi-scalar field model it can be regarded asas a dark energy unify model which describes a variety of asymptoticcosmological scenarios.

Unified dark energy from Chiral-Quintom model with a mixed potential in Friedmann--Lema\^{\i}tre--Robertson--Walker cosmology