Attractor scenarios and superluminal signals in k-essence cosmology

Cosmological scenarios with k-essence are invoked in order to explain the observed late-time acceleration of the Universe. These scenarios avoid the need for fine-tuned initial conditions (the “coincidence problem”) because of the attractorlike dynamics of the k-essence field ϕ. It was recently shown that all k-essence scenarios with Lagrangians p=L(X)ϕ^-2, where X≡1/2ϕ_,μϕ^,μ, necessarily involve an epoch where perturbations of ϕ propagate faster than light (the “no-go theorem”). We carry out a comprehensive study of attractorlike cosmological solutions (“trackers”) involving a k-essence scalar field ϕ and another matter component. The result of this study is a complete classification of k-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form p=K(ϕ)L(X). Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous “no-go theorem” still holds for this class of models, indicating the existence of a superluminal epoch. In the context of k-essence cosmology, the superluminal epoch does not lead to causality violations. We discuss the implications of superluminal signal propagation for possible causality violations in Lorentz-invariant field theories.