k-ESSENCE AND TACHYONS IN BRANEWORLD COSMOLOGY

We investigate a k-essence field localized on the brane evolving linearly with the cosmological time for some kinetic functions and consider the atypical k-essence model for linear and nonlinear k-fields in Friedmann-Robertson-Walker (FRW) cosmology. In the former case the k-field is driven by an inverse quadratic polynomial potential and the solutions exhibit several different behaviors which include expanding, contracting and bouncing universes as well as a model with a finite time span, some of them ending in a big crunch or a big rip. In the latter case we find the potential and show that the atypical k-essence model is dynamically incomplete. Particularly, by selecting the extended tachyonic kinetic functions we analyze the high and low energy limits of our model, obtaining the nearly power-law solution. We introduce a tachyon field with negative energy density and show that the universe evolves between two singularities.