Cosmology dependence of galaxy cluster scaling relations
  The abundance of galaxy clusters as a function of mass and redshift is a well
known powerful cosmological probe, which relies on underlying modelling
assumptions on the mass-observable relations (MOR). Some of the MOR parameters
can be constrained directly from multi-wavelength observations, as the
normalization at some reference cosmology, the mass-slope, the redshift
evolution and the intrinsic scatter. However, the cosmology dependence of MORs
cannot be tested with multi-wavelength observations alone. We use {\tt
Magneticum} simulations to explore the cosmology dependence of galaxy cluster
scaling relations. We run fifteen hydro-dynamical cosmological simulations
varying $\Omega_m$, $\Omega_b$, $h_0$ and $\sigma_8$ (around a reference
cosmological model). The MORs considered are gas mass, baryonic mass, gas
temperature, $Y$ and velocity dispersion as a function of virial mass. We
verify that the mass and redshift slopes and the intrinsic scatter of the MORs
are nearly independent of cosmology with variations significantly smaller than
current observational uncertainties. We show that the gas mass and baryonic
mass sensitively depends only on the baryon fraction, velocity dispersion and
gas temperature on $h_0$, and $Y$ on both baryon fraction and $h_0$. We
investigate the cosmological implications of our MOR parameterization on a mock
catalog created for an idealized eROSITA-like experiment. We show that our
parametrization introduces a strong degeneracy between the cosmological
parameters and the normalization of the MOR. Finally, the parameter constraints
derived at different overdensity ($\Delta_{500c}$), for X-ray bolometric gas
luminosity, and for different subgrid physics prescriptions are shown in the
appendix.
