Constraining hydrostatic mass bias and cosmological parameters with the gas mass fraction in galaxy clusters

The gas mass fraction in galaxy clusters is a convenient tool to use in the context of cosmological studies. Indeed this quantity allows to constrain the universal baryon fraction $\Omega_b/\Omega_m$, as well as other parameters like the matter density $\Omega_m$, the Hubble parameter $h$ or the Equation of State of Dark Energy $w$. This gas mass fraction is also sensitive to baryonic effects that need to be taken into account, and that translate into nuisance parameters. Two of them are the depletion factor $\Upsilon$, and the hydrostatic mass bias $B = (1 - b)$. The first one describes how baryons are depleted in clusters with respect to the universal baryon fraction, while the other encodes the bias coming from the fact that the mass is deduced from X-ray observations under the hypothesis of hydrostatic equilibrium. We will show preliminary results, obtained using the {\it Planck}-ESZ clusters observed by XMM-{\it Newton}, on both cosmological and cluster parameters. We will notably discuss the investigation on a possible redshift dependence of the mass bias, which is considered to be non-existent in hydrodynamic simulations based on $\Lambda$-CDM, and compare our results with other studies.