Phantom dark-energy models, with $w<-1$, are characterized by a future singularity and therefore a finite lifetime for the universe. Because the future singularity is triggered by the onset of dark-energy domination, the universe spends a significant fraction of its total lifetime in a state for which the dark-energy and matter densities are roughly comparable. We calculate, as a function of $w$, the fraction of the total lifetime of the universe for which the dark-energy and matter densities differ by less than the ratio $r_0$ in either direction. For $r_0=10$, this fraction varies from $1/3$ to $1/8$ as $w$ varies from $-1.5$ to $-1.1$; the fraction is smaller for smaller values of $r_0$. This result indicates that the coincidence problem is significantly ameliorated in phantom-dominated cosmologies with a future singularity.

• Received 1 November 2004

DOI:https://doi.org/10.1103/PhysRevD.71.063519