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

Internal space structure generalization of the quintom cosmological scenario