  Luminous matter produces very energetic events, such as active galactic
nuclei and supernova explosions, that significantly affect the internal regions
of galaxy clusters. Although the current uncertainty in the effect of baryonic
physics on cluster statistics is subdominant as compared to other systematics,
the picture is likely to change soon as the amount of high-quality data is
growing fast, urging the community to keep theoretical systematic uncertainties
below the ever-growing statistical precision. In this paper, we study the
effect of baryons on galaxy clusters, and their impact on the cosmological
applications of clusters, using the Magneticum suite of cosmological
hydrodynamical simulations. We show that the impact of baryons on the halo mass
function can be recast in terms on a variation of the mass of the halos
simulated with pure N-body, when baryonic effects are included. The halo mass
function and halo bias are only indirectly affected. Finally, we demonstrate
that neglecting baryonic effects on halos mass function and bias would
significantly alter the inference of cosmological parameters from
high-sensitivity next-generations surveys of galaxy clusters.
