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). MOR parameters have to be simultaneously fit together with the parameters describing the cosmological model. 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 Magneticum simulations to explore the cosmology dependence of galaxy cluster scaling relations. We run fifteen different hydro-dynamical cosmological simulations varying $\Omega_m$, $\Omega_b$, $h_0$ and $\sigma_8$ (around a reference cosmological model). The MORs considered in this work are gas mass, gas temperature, Y and velocity dispersion as a function of the spherical overdensity 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 sensitively depends only on the baryon fraction, velocity dispersion and gas temperature sensitively depend on the hubble constant, and Y depends on both baryon fraction and the hubble constant. 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, degeneracy that can be broken by combining multiple observables and hence improve the cosmological parameter constraints.