Probing neutrino and dark matter properties with stage IV surveys

Beyond the well-known role of neutrino masses, several non-minimal but easy-to-motivate properties of Dark Matter could be tested with forthcoming cosmological surveys - including, for the dominant Dark Matter component, a possible velocity dispersion, a slow decay, or feeble interactions. Using recent forecasts, I will show that Stage-IV surveys like DESI or Euclid have a significant potential of discovery. I will highlight the theoretical challenges that need to be overcome in order to derive robust conclusions from the data.