Dark-Energy Evolution Across the Cosmological-Constant Boundary

Abstract

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.

Figures (1)

• Figure 1: The equation-of-state $w(a)$ for two toy models which cross the cosmological-constant boundary are shown. EOS I is the dashed line, and EOS II is the solid curve. In both cases, dark energy evolves into the phantom regime, below the dot-dashed line, beginning from $a_\star = 1/2$. For EOS II the dark energy evolves as matter at early times, since $w\to 0$, and contributes measurably to the energy budget of the Universe throughout matter domination.