Internal space structure generalization of the quintom cosmological scenario

We introduce the Lagrangian for a multi-scalar field configuration in a $N$-dimensional internal space endowed with a constant metric $Q_{ik}$ and generalize the quintom cosmological scenario. We find the energy momentum tensor of the model and show that the set of dual transformations, that preserve the form of the Einstein equations in the Friedmann-Robertson-Walker (FRW) cosmology, is enlarged. We show that the stability of the power law solutions leads to an exponential potential which is invariant under linear transformations in the internal space. Moreover, we obtain the general exact solution of the Einstein-Klein-Gordon equations for that potential. There exist solutions that cross the phantom divide and solutions that blow up at a finite time, exhibiting a superaccelerated behavior and ending in a big rip. We show that the quintom model with a separable potential can be identified with a mixture of several fluids. This framework includes the $\Lambda$CDM model, a bouncing model, and a setting sourced by a cosmic string network plus a cosmological constant. The we concentrate on the case where the dimension of the internal quintessence sector $N_{q}$ exceeds the dimension of the internal phantom sector $N_{ph}$. For $(N_q,N_{ph})=(2,1)$ the dark energy density derived from the 3-scalar field crosses the phantom divide and its negative component plays the role of the negative part of a classical Dirac Field.