Cosmologies with scalar fields from higher dimensions: K-essence like fields

In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus a la Kaluza-Klein. The corresponding action in four dimensions is similar to that of K-essence theories. This approach is applied to anisotropic cosmological Bianchi type VI(h=-1) model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process, in the epoch to stiff matter with barotropic perfect fluid.