Title: Cluster density slopes from Dark Matter-Baryons Energy Transfer

Abstract: In this paper, we extend previous works on the relation between mass and the inner slope in dark matter density profiles. We calculate that relation in the mass range going from dwarf galaxies to cluster of galaxies. This was done thanks to a modeling of energy transfer via SN and AGN feedback, as well as via dynamical friction of baryon clumps. We show that, in the mass range above galaxy masses (Groups and clusters), the inner slope-mass relation changes its trend. It flattens (towards less cuspy profile) around masses corresponding to groups of galaxies and steepens again for large galaxy cluster masses. The flattening is produced by the AGN outflows (AGN feedback). The one-$ \sigma$ scatter on $\alpha$ is approximately constant in all the mass range ($\Delta\alpha\simeq 0.3$). This is the first paper extending the inner density profile slope-mass relationship to clusters of galaxies, accounting for the role of baryons. The result can be used to obtain a complete density profile, also taking baryons into account. Such kind of density profile was previously only available for galaxies.