Atypical k-essence cosmologies

Abstract

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 when k-essence is the only source 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 and prove the asymptotic stability of the most interesting solutions belonging to the divergent theory. Then, we discuss the implications having not just k-essence but also matter. This is interesting because introducing another component breaks the rigidity of the theory, and the form of the potential ceases to be unique as happened in the pure k-essence case. Finally, we show the finiteness of the effective sound speed under an appropiate definition.

16 pages, new sections investigating the effects of k-essence with a matter component and calculation of perturbations

References in corpus (6)

• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Purely kinetic k-essence as unified dark matter
• Extended tachyon field, Chaplygin gas and solvable k-essence cosmologies
• Power-law expansion in k-essence cosmology
• K-essence and the coincidence problem
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• An exotic k-essence interpretation of interactive cosmological models