Cosmological solutions in multiscalar field theory

We consider a cosmological model with two scalar fields minimally coupled to gravity which have a mixed kinetic term. Hence, Chiral cosmology is included in our analysis. The coupling function and the potential function, which depend on one of the fields, characterize the model we study. We prove the existence of exact solutions that are of special interest for the cosmological evolution. Furthermore, we provide with a methodology that relates the scale factor behaviour to the free functions characterizing the scalar field kinetic term coupling and potential. We derive the necessary conditions that connect these two functions so that the relative cosmological solutions can be admitted. We find that unified dark matter and dark energy solutions are allowed by the theory in various scenarios involving the aforementioned functions.