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

TL;DR

The paper updates cosmological parameter constraints by combining CCCP X-ray cluster data with Planck CMB observations and external probes, exploring three non-vanilla extensions to ΛCDM where the summed neutrino mass is free. It finds strong evidence for a non-zero $\Sigma m_\nu$ (>3$\sigma$) and reveals tensions in $\sigma_8$, the CMB lensing amplitude $A_L$, and the dark-energy equation of state $w$ when X-ray and Planck data are joined. A $9\%$ systematic shift in cluster mass functions can partially alleviate these tensions, but full reconciliation likely requires either unidentified systematics or new physics. The results highlight the sensitivity of late-time structure growth and lensing signals to neutrino masses and cluster mass calibrations, with implications for future cluster and CMB analyses.

Abstract

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$σ$ 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 $σ_8$, X-ray cluster data favor a lower value compared with {\it Planck}. Because of the strong $σ_8-\sum m_ν$ degeneracy, this tension could beyond 2$σ$ confidence level when the summed neutrino mass $\sum m_ν$ is allowed to vary. For the CMB lensing amplitude $A_L$, the addition of X-ray cluster data results in a 3$σ$ 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 $2σ$ 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.

Figures (4)

• Figure 1: Left: Likelihood contours (68% CL and 95% CL) in the $\sum m_{\nu}$--$N_{\mathrm{eff}}$ plane for the Planck+WP+BAO+$H_{0}$+$CL_{\rm {X-ray}}$(red) and Planck+WP+BAO+$H_{0}$ (blue) data combinations. Middle: $\sum m_{\nu}$--$w$ likelihood contours. Right: $\sum m_{\nu}$--$\Omega_{K}$ likelihood contours.
• Figure 2: Triangle likelihood contours of $\sigma_8$, $\sum m_{\nu}$ and $A_L$ with Planck+WP+BAO+HST+$CL_{\rm X-ray}$.
• Figure 3: Left: Marginalized likelihoods of $\sigma_8$. Right: 2D likelihood contours between the lensing amplitude $A_{L}$ and rms amplitude of linear fluctuation $\sigma_{8}$.
• Figure 4: Left: marginalized likelihood of $H_0$ for $w$CDM+$\Sigma{m_\nu}$ (solid) and $\Lambda$CDM+$\Sigma{m_\nu}$+$\Omega_{K}$ (dashed) model. Right: 2D likelihood contours in the $H_0-w$ plane.