k-essence and extended tachyons in brane-worlds

We study a k-essence field evolving linearly with the cosmic time and the atypical k-essence model on a homogeneous and isotropic flat 3-brane. We show that the k-field is driven by an inverse quadratic polynomial potential. The solutions represent expanding, contracting or bouncing universes with a finite time span and some of them end in a big crunch or a big rip. Besides, 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.