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. We study the evolution of the scale factor and address the question of the possible existence of finite-time future singularities. Furthermore, we analyze the evolution of the luminosity distance d _L with redshift z by comparing (normalizing) it with the Λ CDM model. Since the equation of state parameter is z-dependent the evolution of the luminosity distance is also analyzed using the Alcock–Paczyński test.