Distance priors from Planck and dark energy constraints from current data

We derive distance priors from Planck first data release, and examine their impact on dark energy constraints from current observational data. We give the mean values and covariance matrix of {R,l_a,Ω_bh²,n_s}, which give an efficient summary of Planck data. The cosmic microwave background shift parameters are R=Ω_mH_o²r(z_*), and l_a=πr(z_*)/r_s(z_*), where z_* is the redshift at the last scattering surface, and r(z_*) and r_s(z_*) denote our comoving distance to z_* and sound horizon at z_* respectively. We find that Planck distance priors are significantly tighter than those from WMAP9. However, adding Planck distance priors does not lead to significantly improved dark energy constraints using current data, compared to adding WMAP9 distance priors. This is because Planck data appear to favor a higher matter density and lower Hubble constant, in tension with most of the other current cosmological data sets. Adding Planck distance priors to current data leads to a marginal inconsistency with a cosmological constant in a flat universe.