tokens: are not very important for this discussion. The effect of number counts magnification is small compared to WL, RSD, or BAO. For F x B :All magnification only increase FoM γ with , while the effect is a 15 per cent increase for F x B :Counts. This discussion therefore focuses on the number counts results (Counts). In F x B -〈 FB 〉 the surveys overlap, which gives sample variance cancellations, but it does not include the Bright–Faint cross-correlations. This reduces the bias constraints and therefore the magnification constraints. The non-overlapping surveys (F+B) does not have sample variance cancellations from overlapping volumes and there the ratio drops further. Finally, could the low magnification effect be caused by a strong covariance between the counts–shear and magnification signals? The F x B -〈δ γ〉 line is F x B :All, but without all counts-shear cross-correlations or equivalently F x B :Counts adding shear–shear. The effect of magnification is also low when only including the shear-shear lensing observables. A lower Faint bias amplitude improves the forecast. One can understand this from a signal-to-noise argument. The variance (Δ 2 ) of the magnification signal when assuming Gaussian fluctuations (equation 3 ) is where i and j are the two redshift bins. The auto-correlation terms dominate for well separated bins in photo-z space, which leads to the approximation in the second line. If ignoring RSD, the magnification–magnification correlations and the shot-noise, the magnification signal-to-noise is where α j and b j are, respectively, the magnification slope and the galaxy bias in redshift bin j . The and terms are the matter auto-correlations in bin i and j , respectively. This approximation is invalid for low Faint bias amplitudes. Equation ( A4 ) shows two important criteria for magnification. A higher magnification slope increase the signal, while a lower bias of the background population decrease the errors. This criteria can be useful if focusing solely on magnification. However, one should focus on RSD, BAO, and WL for the combined constraints, since these effects give stronger cosmology constraints. APPENDIX B: PHOTOMETRIC REDSHIFTS AND GALAXY DENSITIES B1 Photometric redshifts The bias measurements are also affected by redshift uncertainties. Our two fiducial galaxy samples are: a photometric (Faint) and a spectroscopic (Bright) with respectively 0.05(1 + ) and 0.001(1 + ) Gaussian redshift uncertainties. The Faint sample is analysed in broad redshift bins since the Faint photo-z is broad. Improving the Faint photo-z would only substantially change the forecast if also using narrow bins for the Faint sample. We focus instead on the Bright redshift uncertainty and fix the Faint photo-z to the fiducial value. Fig. B1 shows the F x B :All Bright bias error ratios between the case of using spectroscopic (Bright) sample and the case of including redshift uncertainties (photo-z) in the Bright sample. A vertical line (0.0035)
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