Reconstruction of nonlinear power spectrum. For each model, we reconstruct P_NL(k) (solid lines) from the estimation of σ_NL(M) deduced from shape measures of DM halos at z = 0. The thickness of the solid line reflects an imprecision of 5% on the true value of the density parameter Ω_m assumed from independent measurements. The expected nonlinear power spectrum and linear power spectrum deduced from the cosmic matter field of numerical simulation are respectively in dotted line, and dashed line. The agreement between the nonlinear power spectrum and the reconstructed power spectrum is excellent.