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We derived constraints on cosmological parameters using weak lensing peakstatistics measured on the $\sim130~{\rm deg}^2$ of the Canada-France-HawaiiTelescope Stripe 82 Survey (CS82). This analysis demonstrates the feasibilityof using peak statistics in cosmological studies. For our measurements, weconsidered peaks with signal-to-noise ratio in the range of $\nu=[3,6]$. For aflat $\Lambda$CDM model with only $(\Omega_{\rm m}, \sigma_8)$ as freeparameters, we constrained the parameters of the following relation$\Sigma_8=\sigma_8(\Omega_{\rm m}/0.27)^{\alpha}$ to be: $\Sigma_8=0.82 \pm0.03 $ and $\alpha=0.43\pm 0.02$. The $\alpha$ value found is considerablysmaller than the one measured in two-point and three-point cosmic shearcorrelation analyses, showing a significant complement of peak statistics tostandard weak lensing cosmological studies. The derived constraints on$(\Omega_{\rm m}, \sigma_8)$ are fully consistent with the ones from eitherWMAP9 or Planck. From the weak lensing peak abundances alone, we obtainedmarginalised mean values of $\Omega_{\rm m}=0.38^{+0.27}_{-0.24}$ and$\sigma_8=0.81\pm 0.26$. Finally, we also explored the potential of using weaklensing peak statistics to constrain the mass-concentration relation of darkmatter halos simultaneously with cosmological parameters.

Cosmological Constraints From Weak Lensing Peak Statistics With CFHT Stripe 82 Survey