We present a Bayesian approach to combine Planck data and the X-ray physical properties of the intracluster medium in the virialization region of a sample of 320 galaxy clusters ( 0.056 < z < 1.24 , kT \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 3 keV ) observed with Chandra .
We exploited the high-level of similarity of the emission measure in the cluster outskirts as cosmology proxy .
The cosmological parameters are thus constrained assuming that the emission measure profiles at different redshift are weakly self-similar , that is their shape is universal , explicitly allowing for temperature and redshift dependence of the gas fraction .
This cosmological test , in combination with Planck +SNIa data , allows us to put a tight constraint on the dark energy models .
For a constant- w model , we have w = -1.010 \pm 0.030 and \Omega _ { m } = 0.311 \pm 0.014 , while for a time-evolving equation of state of dark energy w ( z ) we have \Omega _ { m } = 0.308 \pm 0.017 , w _ { 0 } = -0.993 \pm 0.046 and w _ { a } = -0.123 \pm 0.400 .
Constraints on the cosmology are further improved by adding priors on the gas fraction evolution from hydrodynamic simulations .
Current data favour the cosmological constant with w \equiv - 1 , with no evidence for dynamic dark energy .
We checked that our method is robust towards different sources of systematics , including background modelling , outlier measurements , selection effects , inhomogeneities of the gas distribution and cosmic filaments .
We also provided for the first time constraints on which definition of cluster boundary radius is more tenable , namely based on a fixed overdensity with respect to the critical density of the Universe .
This novel cosmological test has the capacity to provide a generational leap forward in our understanding of the equation of state of dark energy .