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.
