Anisotropic k-essence cosmologies

We investigate a Bianchi type-I (BTI) cosmology with k essence and find the set of models which dissipate the initial anisotropy. There are cosmological models with extended tachyon fields and k essence having constant bariotropic index. We obtain the conditions leading to a regular bounce of the average geometry and the residual anisotropy on the bounce. For constant potential, we develop purely kinetic k-essence models which are dust dominated in their early stages, dissipate the initial anisotropy and end in a stable de Sitter accelerated expansion scenario. We show that linear k field and polynomial kinetic function models evolve asymptotically to Friedmann-Robertson-Walker (FRW) cosmologies. The linear case is compatible with an asymptotic potential interpolating between $V_l\propto \phi^{-\gamma_l}$, in the shear dominated regime, and $V_l\propto\phi^{-2}$ at late time. In the polynomial case, the general solution contains cosmological models with an oscillatory average geometry. For linear k essence, we find the general solution in the BTI cosmology when the k field is driven by an inverse square potential. This model shares the same geometry than a quintessence field driven by an exponential potential.