Dark Energy Constraints after Planck

Abstract: The Planck collaboration has recently published maps of the Cosmic Microwave Background radiation with the highest precision. In the standard flat $\Lambda$CDM framework, Planck data show that the Hubble constant $H_0$ is in tension with that measured by the several direct probes on $H_0$. In this paper, we perform a global analysis from the current observational data in the general dark energy models and find that resolving this tension on $H_0$ requires the dark energy model with its equation of state (EoS) $w\neq-1$. Firstly, assuming the $w$ to be a constant, the Planck data favor $w < -1$ at about $2\,\sigma$ confidence level when combining with the supernovae "SNLS" compilation. And consequently the value derived on $H_0$, $H_0=71.3\pm2.0$ ${\rm km\,s^{-1}\,Mpc^{-1}}$ (68% C.L.), is consistent with that from direct $H_0$ probes. We then investigate the dark energy model with a time-evolving $w$, and obtain the 68% C.L. constraints $w_0=-0.81\pm0.19$ and $w_a=-1.9\pm1.1$ from the Planck data and the "SNLS" compilation. Current data still slightly favor the Quintom dark energy scenario with EoS across the cosmological constant boundary $w\equiv-1$.