Cosmological parameter estimation from CMB and X-ray clusters after Planck

We update the cosmological parameter estimation for three non-vanilla models by a joint analysis of \CCCP\ X-ray cluster, the newly released \Planck\ CMB data as well as some external data sets, such as baryon acoustic oscillation measurements from the 6dFGS, SDSS DR7 and BOSS DR9 surveys, and Hubble Space Telescope $H_0$ measurement. First of all, we find that X-ray cluster data sets strongly favor a non-zero summed neutrino mass at more than 3$\sigma$ confidence level in these non-vanilla models. And then, we reveal some tensions between X-ray cluster and {\it Planck} data in some cosmological parameters. For the matter power spectrum amplitude $\sigma_8$, X-ray cluster data favor a lower value compared with {\it Planck}. Because of the strong $\sigma_8-\sum m_{\nu}$ degeneracy, this tension could beyond 2$\sigma$ confidence level when the summed neutrino mass $\sum m_{\nu}$ is allowed to vary. For the CMB lensing amplitude $A_L$, the addition of X-ray cluster data results in a 3$\sigma$ deviation from the vanilla model. Furthermore, {\it Planck}+X-ray data prefer a large Hubble constant and phantom-like dark energy equation of state, which are in $2\sigma$ tension with those from WMAP7+X-ray data. Finally, we find that these tensions/descrepencies could be relaxed in some sense by adding a $9\%$ systematic shift in the cluster mass functions.