An equation of state for purely kinetic k-essence inspired by cosmic
  topological defects
  We investigate the physical properties of a purely kinetic k-essence model
with an equation of state motivated in superconducting membranes. We compute
the equation of state parameter $w$ and discuss its physical evolution via a
nonlinear equation of state. Using the adiabatic speed of sound and energy
density, we restrict the range of parameters of the model in order to have an
acceptable physical behavior. Furthermore, we analyze the evolution of the
luminosity distance $d_{L}$ with redshift $z$ by comparing (normalizing) it
with the $\Lambda$CDM model. Since the equation of state parameter is
$z$-dependent the evolution of the luminosity distance is also analyzed using
the Alcock-Paczy\'{n}ski test.
