Atypical k-essence cosmologies

We analyze the implications of having a divergent speed of sound in k-essence cosmological models. We first study a known theory of that kind, for which the Lagrangian density depends linearly on the time derivative of the k-field. We show that consistency requires that the potential of the k-field be of the inverse square form. Then, we review the known result that the corresponding power-law solutions can be mapped to power-law solutions of theories with no divergence in the speed of sound. After that, we argue that the requirement of a divergent sound speed at some point fixes uniquely the form of the Lagrangian to be exactly the one considered earlier. Finally, we prove the asymptotic stability of the most interesting solutions belonging to the divergent theory. ∗[email protected] ∗∗[email protected]