Exact Solutions in Chiral Cosmology

In multi-scalar field cosmologies new dynamical degrees of freedom are introduced which can explain the observational phenomena. Unlike the usual scalar field theory where a single scalar field is considered, the multi-scalar field cosmologies allow more than one scalar field and exhibits interetsing consequences, such as quintom, hybrid inflation etc. The current work studies the existence of exact solutions and integrable dynamical systems in multi-scalar field cosmology. We present the exact analytic solutions for a system of $N$-scalar fields. In particular, we consider a multi scalar field cosmological scenario comprised of $N$-scalar fields that are minimally coupled to the Einstein gravity. The geometry of the universe is described by the spatially flat homogeneous and isotropic line element and the scalar fields may interact in their kinetic or/and potential terms. Within this set up, we show that for a specific geometry in the kinetic part of the scalar fields and specific potential form, the gravitational field equations for the class of $N$-scalar field models can be exactly solved. More specifically, we show that the Einstein field equations in $N$-scalar field cosmology can be reduced to that of a $\left( N+1\right)$ linear system.