Internal space structure generalization of the quintom cosmological scenario

Understand

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.