Dark-energy evolution across the cosmological-constant boundary

We explore the properties of dark-energy models for which the equation of state, $w$, defined as the ratio of pressure to energy density, crosses the cosmological-constant boundary $w=-1$. We adopt an empirical approach, treating the dark energy as an uncoupled fluid or a generalized scalar field. We describe the requirements for a viable model, in terms of the equation of state and sound speed. A generalized scalar field cannot safely traverse $w=-1$, although a pair of scalars with $w>-1$ and $w<-1$ will work. A fluid description with a well-defined sound speed can also cross the boundary. Contrary to expectations, such a crossing model does not instantaneously resemble a cosmological constant at the moment $w=-1$ since the density and pressure perturbations do not necessarily vanish. But because a dark energy with $w<-1$ dominates only at very late times, and because the dark energy is not generally prone to gravitational clustering, then crossing the cosmological-constant boundary leaves no distinct imprint.