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.
