Histograms of aperture mass statistics for ΛCDM and f5(R) models with varying neutrino mass mν. Each histogram, with area normalised to one, comprises 256 samples of the statistic computed at a filtering scale of ϑ = 0.586′ and for sources at redshift zs = 2.0. Solid lines represent the result of smoothing the distribution by KDE (cf. Sect. 5.3). The central positions of the histograms correspond to the mean values of each statistic as seen in Figs. 5–7. Considering the most degenerate case with ΛCDM, f5(R) with mν = 0.15 eV, second- and higher-order moments of Map do not appear able to distinguish the models. Peak counts, on the other hand, shown here for a 3σ threshold, cleanly separate the two distributions. Moreover, it is interesting that peak counts separate all f5(R) cases from ΛCDM by approximately the same amount, independent of mν.
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