We reexamine $k$-essence dark energy models with a scalar field $\varphi$ and a factorized Lagrangian, $\mathcal{L}=V(\varphi )F(X)$, with $X=\frac{1}{2}{\nabla }_{\mu }\varphi {\nabla }^{\mu }\varphi$. A value of the equation of state parameter, $w$, near $-1$ requires either $X\approx 0$ or $dF/dX\approx 0$. Previous work showed that thawing models with $X\approx 0$ evolve along a set of unique trajectories for $w(a)$, while those with $dF/dX\approx 0$ can result in a variety of different forms for $w(a)$. We show that if $dV/d\varphi$ is small and $(1/V)(dV/d\varphi )$ is roughly constant, then the latter models also converge toward a single unique set of behaviors for $w(a)$, different from those with $X\approx 0$. We derive the functional form for $w(a)$ in this case, determine the conditions on $V(\varphi )$ for which it applies, and present observational constraints on this new class of models. We note that $k$-essence models with $dF/dX\approx 0$ correspond to a dark energy sound speed $c_s^2\approx 0$.

• Received 15 May 2019

DOI:https://doi.org/10.1103/PhysRevD.100.023525