Probing dark energy dynamics from current and future cosmological observations

We report the constraints on the dark energy equation-of-state $w(z)$ using the latest “Constitution” SNe sample combined with the WMAP5 and Sloan Digital Sky Survey data. Assuming a flat Universe, and utilizing the localized principal component analysis and the model selection criteria, we find that the $\Lambda \mathrm{CDM}$ model is generally consistent with the current data, yet there exists a weak hint of the possible dynamics of dark energy. In particular, a model predicting $w(z)<-1$ at $z\in [0.25,0.5)$ and $w(z)>-1$ at $z\in [0.5,0.75)$, which means that $w(z)$ crosses $-1$ in the range of $z\in [0.25,0.75)$, is mildly favored at 95% confidence level. Given the best fit model for current data as a fiducial model, we make future forecast from the joint data sets of Joint Dark Energy Mission, Planck, and Large Synoptic Survey Telescope, and we find that the future surveys can reduce the error bars on the $w$ bins by roughly a factor of 10 for a 5-$w$-bin model.

Figure 1

The correlated binned estimates of the EoS from current observational data. The inner black and outer red error bars show $1\sigma$ and $2\sigma$ uncertainties, respectively. The blue dashed line shows $\Lambda \mathrm{CDM}$ model.

Figure 2

The improved ${\chi }^2$ and reduced ${\chi }^2$ with respect to the $\Lambda \mathrm{CDM}$ model as a function of the number of $w$ bins. The big red stars illustrate the optimal model.

Figure 3

The correlation matrices for the $w$ bins for different binnings. From upper left to lower right, we show the correlation matrices for $N=2$ to $N=10$ binnings (high-$z$ bin inclusive in all cases, as stated in the main text).

Figure 4

Panel (A, B): The reconstructed $w(z)$ and $q(z)$ using 5 bins from current data. The vertical black and red error bars show $1\sigma$ and $2\sigma$ errors, respectively. The blue dashed line shows $\Lambda \mathrm{CDM}$ model; Panel (C): The rescaled window function $\mathcal{W}$; Panel (D): One-dimensional probability distribution of the $q$’s.

Figure 5

Future forecasts from $\mathrm{JDEM}+\mathrm{\text{Planck}}+\mathrm{LSST}$ on $w(z)$, $q(z)$ and the window functions. Left panels: Forecasts including statistical errors only; Right: Statistical plus systematic errors. The legends are the same as that for panels (A–C) in Fig. 4.

Figure 6

Left: Comparison of the reconstructed $w(z)$ using two different parametrizations. The 68% (black) and 95%(red) C.L. error bars show the reconstructed $w(z)$ using parametrization ${\mathcal{X}}_{\mathrm{I}}$; The shaded regions show the $w(z)$ reconstruction using parametrization ${\mathcal{X}}_{\mathrm{II}}$. The inner and outer shades illustrate the 68% and 95% C.L. errors, respectively, and central white line show the best fit model; Right: Contour plots for $w_0$, $w_a$. Grey: current data; Yellow: forecast from $\mathrm{JDEM}+\mathrm{\text{Planck}}+\mathrm{LSST}$ with systematics; Blue: forecast without systematics. For the same color, the dark and light shaded regions denote the 68% and 95% C.L. contours, respectively. The red star stands for the $\Lambda \mathrm{CDM}$ model, and the white cross illustrates the current best fit model.