Examining the Evidence for Dynamical Dark Energy

We apply a new nonparametric Bayesian method for reconstructing the evolution history of the equation of state $w$ of dark energy, based on applying a correlated prior for $w(z)$, to a collection of cosmological data. We combine the latest supernova (SNLS 3 year or Union 2.1), cosmic microwave background, redshift space distortion, and the baryonic acoustic oscillation measurements (including BOSS, WiggleZ, and 6dF) and find that the cosmological constant appears consistent with current data, but that a dynamical dark energy model which evolves from $w<-1$ at $z\sim 0.25$ to $w>-1$ at higher redshift is mildly favored. Estimates of the Bayesian evidence show little preference between the cosmological constant model and the dynamical model for a range of correlated prior choices. Looking towards future data, we find that the best fit models for current data could be well distinguished from the $\Lambda \mathrm{CDM}$ model by observations such as Planck and Euclid-like surveys.

Figure 1

Panels (A1)-(A4): The best fit $w(z)$ with marginalized 68% and 95% C.L. error (shaded bands) reconstructed from a joint data set of the latest data including SN, CMB, $H(z)$, RSD and BAO. This best fit $w(z)$ is used to construct mock data for future Planck and Euclid-like surveys, and the resulting reconstruction is shown by the magenta dots (with 68% C.L. error bars). The four panels show the result using different combinations of priors (standard and weak) and supernovae data sets (SNLS3 and Union2.1). (B1)-(B4): The 68% C.L. constraints on $w(z)$ using different data subsets: $\mathrm{SN}+\mathrm{CMB}+H(z)$(black solid), adding RSD (magenta dashed), adding $\mathrm{RSD}+\mathrm{BAO}$ (blue band). (C1), (C2): These reconstructed models affect the fit to the BAO and RSD data; we compare the reconstruction from the combined data (using SNLS3 and weak prior) with the $\Lambda \mathrm{CDM}$ model (green dashed).

Figure 2

Panels (A1), (A2): Eigenvalues of the covariance matrix of the $w$ bins obtained from the data plus prior (diamonds and circles) and prior alone (shaded region) using MCMC. (B1), (B2): The first 3 (4) data-dominated eigenmodes of the covariance matrices. These panels show only small differences arise when different SN data sets are combined with other data. Results for the standard prior and weak prior are shown separately. Panels (C1) and (C2) show the improved likelihood ($\Delta \ln L$), the reduced fraction of the sampled parameter space ($\Delta \ln V$), and the logarithm of the evidence ratio as a function of ${\sigma }_{\mathrm{bin}}$ relative to the $\Lambda \mathrm{CDM}$ model (which is the small ${\sigma }_{\mathrm{bin}}$ limit.) (C1) and (C2) are for the present data (SNLS3) and the simulated Planck and Euclid-like data, respectively.