Physical Review D - Particles, Fields, Gravitation, and Cosmology
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.
Caldwell, Robert R. and Doran, Michael, "Dark-Energy Evolution Across the Cosmological-Constant Boundary" (2005). Open Dartmouth: Faculty Open Access Articles. 1975.