Slow-roll k-essence

Abstract

We derive slow-roll conditions for thawing k-essence with a separable Lagrangian $p(X,\varphi )=F(X)V(\varphi )$. 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 $X\approx 0$ and $F_X\approx 0$, respectively. For the case where $X\approx 0$ the evolution of $\varphi$ 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 non-separable Lagrangians where $X\approx 0$. For the case $F_X\approx 0$, an expression is derived for $w(a)$, but this expression depends on the potential $V(\varphi )$, so there is no model-independent limiting behavior. For the $X\approx 0$ case, we derive observational constraints on the two parameters of the model, $w_0$ (the present-day value of $w$), and the $K$, which parametrizes the curvature of the potential. We find that the observations sharply constrain $w_0$ to be close to -1, but provide very poor constraints on $K$.

Comments: 7 pages and 5 figures, typos corrected