tokens: from 108 full-sky maps (Takahashi et al. 2017 ; Namikawa et al. 2019 ). The error bars are the standard deviations scaled by . The solid red, dashed orange, and dotted brown curves are the theoretical predictions based on BiHalofit, GM12 , and SC01 , respectively. The middle panels plot the relative deviations from the red curves: . In the bottom panels, these deviations are further divided by the relative standard deviation (). Although our fitting surely improved the prediction accuracy, noticeable discrepancies from the simulations were introduced by several sources. First, the finite thickness of the lens planes employed in the ray-tracing simulations may affect the simulations at l 200 (the same effect on convergence PS is demonstrated in Figure 10 of Takahashi et al. 2017 ). Second, the flat-sky formula in Equation ( 16 ) is inaccurate at large angular scales (the accuracy of the flat-sky approximation in the cosmic-shear PS is detailed in Kilbinger et al. 2017 ; Kitching et al. 2017 ). For example, in the squeezed limit, the minimum multipole is fixed as l 3 = 50, but a larger l 3 can mitigate the discrepancy (Namikawa et al. 2019 ). Since reducing the finite thickness of lens planes requires more numerically expensive simulations, we will leave the detailed study for future work. 6.2. Cosmic Shear Let us now consider the cosmic-shear signals in galaxy-shape measurements, which probe lower redshifts than CMB lensing. Sato et al. ( 2009 ) ran cosmological N -body simulations and subsequent ray-tracing simulations under the flat-sky approximation. Despite their small field of view (5 × 5 deg 2 ), they acquired sufficiently many weak-lensing maps (1000) for an accurate BS measurement. Their cosmological model was consistent with the WMAP 3 yr result (Spergel et al. 2007 ). Figure 13 plots the convergence BS at a source redshift of z s = 1, measured from the 1000 maps by Kayo et al. ( 2013 ). The theoretical and simulation results were consistently binned with . The simulation results were valid (within 5% error) up to l ≃ 4000, as confirmed by comparing the results with those from low- and high-resolution maps (Sato et al. 2009 ; Valageas et al. 2012 ). Overall, the plot shows a similar trend to the matter BS at z = 0.55 (see Figure 5 ). Our fitting formula well agreed with the simulation (within 10% level up to l = 4000). The deviation at small scales ( l ≳ 4000) was attributed to the limited resolution of the simulation. Figure 13. Convergence BSs measured from 1000 simulation maps at the source redshift (Sato et al. 2009 ; Kayo et al. 2013 ). Black circles are the measured averages, and the red curves were predicted by our model. The dashed orange and brown dotted curves were obtained by GM12 and SC01 , respectively. The field of view of each map is , and the error bars are the standard deviations scaled by . The bottom panels plot the relative deviations from the red curves. As the cosmological models in this and the previous
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