Mass-concentration relation and weak lensing peak counts

Context. The statistics of peaks in weak lensing convergence maps is a promising tool for investigating both the properties of dark matter haloes and constraining the cosmological parameters. Aims: We study how the number of detectable peaks and its scaling with redshift depend upon the cluster's dark matter halo profiles and use peak statistics to constrain the parameters of the mass-concentration (MC) relation. We investigate which constraints the Euclid mission can set on the MC coefficients taking degeneracies with the cosmological parameters into account, too. Methods: To this end, we first estimated the number of peaks and its redshift distribution for different MC relations and found that the steeper the mass dependence and the greater the normalisation, the larger the number of detectable clusters, with the total number of peaks changing up to 40% depending on the MC relation. We then performed a Fisher matrix forecast of the errors on the MC relation parameters, as well as on cosmological parameters. Results: We find that peak number counts detected by Euclid can determine the normalization Av, the mass Bv, redshift Cv slopes, and intrinsic scatter σv of the MC relation to an unprecedented accuracy, which is σ(Av) /Av = 1%, σ(Bv) /Bv = 4%, σ(Cv) /Cv = 9%, and σ(σv) /σv = 1% if all cosmological parameters are assumed to be known. If we relax this severe assumption, constraints are degraded, but remarkably good results can be restored by setting only some of the parameters or combining peak counts with Planck data. This precision can give insight into competing scenarios of structure formation and evolution and into the role of baryons in cluster assembling. Alternatively, for a fixed MC relation, future peak counts can perform as well as current BAO and SNeIa when combined with Planck.