Two new diagnostics of dark energy

Abstract

We introduce two new diagnostics of dark energy (DE). The first, $Om$, is a combination of the Hubble parameter and the cosmological redshift and provides a null test of dark energy being a cosmological constant $\ensuremath{\Lambda}$. Namely, if the value of $Om(z)$ is the same at different redshifts, then $\mathrm{DE}\ensuremath{\equiv}\ensuremath{\Lambda}$, exactly. The slope of $Om(z)$ can differentiate between different models of dark energy even if the value of the matter density is not accurately known. For DE with an unevolving equation of state, a positive slope of $Om(z)$ is suggestive of phantom ($wl\ensuremath{-}1$) while a negative slope indicates quintessence ($wg\ensuremath{-}1$). The second diagnostic---acceleration probe $\overline{q}$---is the mean value of the deceleration parameter over a small redshift range. It can be used to determine the cosmological redshift at which the universe began to accelerate, again without reference to the current value of the matter density. We apply the $Om$ and $\overline{q}$ diagnostics to the Union data set of type Ia supernovae combined with recent data from the cosmic microwave background (Wilkinson Microwave Anisotropy Probe 5) and baryon acoustic oscillations.