Cosmology with non-minimally coupled k-field

We consider a non-minimally coupled (with gravity) scalar field with non-canonical kinetic energy. The form of the kinetic term is of Dirac–Born–Infeld form. We study the early evolution of the universe when it is sourced only by the k-field, as well as late time evolution when both the matter and k-field are present. For the k-field, we have considered constant potential as well as potential inspired from boundary string field theory. We show that it is possible to have an inflationary solution in early time as well as late time accelerating phases. The solutions also exhibit attractor properties in a sense that they do not depend on the initial conditions for certain values of the parameters.