New null diagnostic customized for reconstructing the properties of dark energy from baryon acoustic oscillations data

Baryon acoustic oscillations (BAO) provide an important standard ruler which can be used to probe the recent expansion history of our Universe. We show how a simple extension of the $Om$ diagnostic, which we call $Om3$, can combine standard ruler information from BAO with standard candle information from type Ia supernovae (SNIa) to yield a powerful novel null diagnostic of the cosmological constant hypothesis. A unique feature of $Om3$ is that it requires minimal cosmological assumptions since its determination does not rely upon prior knowledge of either the current value of the matter density ${\Omega }_{0m}$ and the Hubble constant $H_0$ or the distance to the last scattering surface. Observational uncertainties in these quantities, therefore, do not affect the reconstruction of $Om3$. We reconstruct $Om3$ using the Union 2.1 SNIa data set and BAO data from SDSS, WiggleZ and 6dFGS. Our results are consistent with dark energy being the cosmological constant. We show how $Om$ and $Om3$ can be used to obtain accurate model-independent constraints on the properties of dark energy from future data sets such as BigBOSS.

Figure 1

The $Om3$ diagnostic (1.9) is shown as a function of separation, $z_3-z_2$, for $z_1=0.2$, $z_2=0.35$ and ${\Omega }_{0m}=0.27$. This diagnostic is clearly able to discriminate quite well between evolving DE models and $\Lambda \mathrm{CDM}$, since for $\Lambda \mathrm{CDM}$ the value of $Om3$ stays pegged at unity, while for Quintessence/Phantom, $Om3$ rapidly evolves to larger/smaller values as the separation $z_3-z_2$ increases.

Figure 2

Two variants of $Om3$ determined using uncorrelated BAO measurements at three redshifts in conjunction with the luminosity distance reconstructed from Union 2.1 SNIa data. The redshift combinations $Om3(0.106,0.35,0.60)$ and $Om3(0.35,0.73,0.106)$ shown in the top left and bottom right panels have the smallest error bars and, therefore, provide the tightest constraints on DE from current $\mathrm{BAO}+\mathrm{SNIa}$ data. The large error bars in the middle panels for $Om3$ are mainly due to the poor estimation of $d(z=0.44)$ (see Table ). The spatially flat $\Lambda \mathrm{CDM}$ model is in good agreement with the data. Note that these results do not rely on a knowledge of ${\Omega }_{0m}$, $H_0$ or the distance to the last scattering surface.

Figure 3

Two variants of $Om3$ derived using simulated realizations of the BigBOSS experiment assuming a fiducial $\Lambda \mathrm{CDM}$ cosmology. Horizontal lines represent different dark energy models with (top-down) $w=-0.8$, $w=-1.0$, $w=-1.2$. ${\Omega }_{0m}=0.27$ is assumed for all models. Note that the determination of $Om3$ requires minimal cosmological assumptions since one does not require a background model to estimate ${\Omega }_{0m}$, $H_0$ or the distance to the last scattering surface. Note also the difference in scale of the $y$ axis relative to Fig. 2.

Figure 4

The $Om$ diagnostic is reconstructed for a single simulated realization of the planned BigBOSS experiment assuming a fiducial $\Lambda \mathrm{CDM}$ cosmology. A determination of $h(z)$, and hence $Om(z)$, from future BAO experiments can clearly help distinguish between rival models of dark energy. Note that this determination is based on values of $H_0$ with 2% uncertainty expected by the time BigBOSS becomes operational.