Distance Priors from \emph{Planck} 2015 data

We update the distance priors by adopting $Planck~ \textrm{TT,TE,EE}+\textrm{lowP}$ data released in 2015, and our results impose at least $30\%$ tighter constraints than those from $Planck~ \textrm{TT}+\textrm{lowP}$. Combining the distance priors with the combination of supernova Union~2.1 compilation of 580 SNe (Union~2.1) and low redshift Baryon Acoustic Oscillation (BAO) data, we constrain the cosmological parameters in the freely binned dark energy (FBDE) and FBDE$+\Omega_k$ models respectively, and find that the equations of state of dark energy in both models are consistent with $w=-1$. Furthermore, we show that the tension with the BAO data at $z=2.34$ from Ly$\alpha$ forest (Ly$\alpha$F) auto-correlation and Combined Ly$\alpha$F cannot be relaxed in the FBDE and FBDE$+\Omega_k$ models.