| Summary: | Abstract 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 $$V\left( \phi ,\psi \right) =V_{0}e^{\lambda \phi }+U_{0}e^{\kappa \phi }\psi ^{\frac{1}{\sigma } }$$ V ϕ , ψ = V 0 e λ ϕ + U 0 e κ ϕ ψ 1 σ and we investigate the asymptotic limits of the cosmological parameters. This model for $$U_{0}=0$$ U 0 = 0 , provides a generalization of the hyperbolic inflation where the equation of the state parameter can cross the phantom divide line. When $$U_{0}\ne 0$$ U 0 ≠ 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.
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