When did cosmic acceleration start?

A precise determination, and comparison, of the epoch of the onset of cosmic acceleration, at redshift $z_{\mathrm{acc}}$, and of dark energy domination, at $z_{\mathrm{eq}}$, provides an interesting measure with which to parametrize dark energy models. By combining several cosmological data sets, we place constraints on the redshift and age of cosmological acceleration. For a $\Lambda \mathrm{CDM}$ model, we find the constraint $z_{\mathrm{acc}}=0.76\pm 0.10$ at 95% C.L., occurring $6.7\pm 0.4\mathrm{Gyr}$ ago. Allowing a constant equation of state but different from $-1$ changes the constraint to $z_{\mathrm{acc}}=0.81\pm 0.12$ ($6.9\pm 0.5\mathrm{Gyr}$ ago), while dynamical models markedly increase the error on the constraint $z_{\mathrm{acc}}=0.81\pm 0.30$ ($6.8\pm 1.4\mathrm{Gyr}$ ago). Unified dark energy models such as silent quartessence yield $z_{\mathrm{acc}}=0.8\pm 0.16$ ($6.8\pm 0.6\mathrm{Gyr}$ ago). Interestingly, we find that the best fit $z_{\mathrm{acc}}$ and $z_{\mathrm{eq}}$ are remarkably insensitive to both the cosmological data sets and theoretical dark energy models considered.

Figure 1

Constraints on the $z_{\mathrm{acc}}–z_{\mathrm{eq}}$ plane for different dark energy parametrizations. From top to bottom: $w$ constant, CPL, HM models. Also plotted (dashed line) is the cosmological constant case $z_{\mathrm{acc}}=2^{1/3}(z_{\mathrm{eq}}+1)-1$.

Figure 2

Constraints at 95% C.L. on the deceleration parameter $q(z)$ as a function of redshift for different dark energy parametrizations (see text).