Slow-roll k-essence

We derive slow-roll conditions for thawing k-essence with a separable Lagrangian p (X, ) =F (X) V (). We examine the evolution of the equation of state parameter, w, as a function of the scale factor a, for the case where w is close to -1. We find two distinct cases, corresponding to X0 and Fₗ0, respectively. For the case where X0 the evolution of and hence w is described by only two parameters, and w (a) is model independent and coincides with similar behavior seen in thawing quintessence models. This result also extends to nonseparable Lagrangians where X0. For the case Fₗ0, an expression is derived for w (a), but this expression depends on the potential V (), so there is no model-independent limiting behavior. For the X0 case, we derive observational constraints on the two parameters of the model, w₀ (the present-day value of w), and the K, which parametrizes the curvature of the potential. We find that the observations sharply constrain w₀ to be close to -1, but provide very poor constraints on K.