tokens: the minimum comoving scale R = 8 h −1 Mpc. This cut is translated to an angular harmonic mode on each tomographic bin using the Limber relation l max = k max × χ(〈 z i 〉), where is the mean redshift for the i th tomographic bin of the analysis and χ( z ) the comoving distance computed on the fiducial cosmology of the analysis. Similar approaches were taken in Nicola et al. ( 2020 ) and Doux et al. ( 2020 ). We fix , which yields l max = 80, 127, 172, 215, and 246 for the five redshift bins for DES-Y1 cosmology. We checked these cuts do not change significantly when using a FLASK cosmology. We also keep l min = 43 for all bins based on the impact of binning for our modelling. In order to verify whether these scale cuts are effective to mitigate the effects of nonlinear bias we perform a simple χ 2 test comparing two data vectors: a fiducial data vector generated with a linear bias and a data vector contaminated with nonlinear bias. More specifically, we generate a contaminated data vector with an additional quadratic bias parametrized as a function of the linear bias as in Lazeyras et al. ( 2016 ). Using the FLASK covariance matrix we find that Δχ 2 = 0.2 for the physical cuts, where well below the criterion Δχ 2 1 adopted in Abbott et al. ( 2019a ). Hence the nonlinear biases as modelled above are mitigated by the physical scale cuts. Just for comparison, for the naive scale cuts, we find that Δχ 2 = 14.31 and therefore this further justifies our fiducial analysis choice for the physical scale cuts. 7 RESULTS ON MOCKS In order to validate our pipeline, we ran the implemented nested sampling algorithm using as input a random mock realization as well as the average of the set of mocks. We explored the parameter space: where b i is the constant linear galaxy bias in the redshift shell z i with a flat prior (0.8 b i 3.0), and Δ z i is the respective shift in the mean of the photometric redshift distribution for each redshift bin i : n i ( z ) → n i ( z − Δ z i ). The Gaussian priors are centred in Δ z i = 0 (for the synthetic data used in this section) and width as in Elvin-Poole et al. ( 2018 ). We use the FLASK covariance matrix as the fiducial one. We show that the CosmoLike theoretical covariance matrix yields very similar results in Fig. 4 . 11 In this section, we use the average of the FLASK mocks as a proxy for a noiseless data vector, as used in simulated likelihood analyses (Krause et al. 2017 ). The use of the FLASK covariance matrix gives the uncertainty one would expect for the real data likelihood analyses, which is the goal of the comparison between the harmonic and configuration space performed in the DES-Y1 data in Section 8 . The recovery of unbiased cosmological parameters in this case also shows that the Gaussian likelihood approximation is adequate. Figure 4. Comparison of the bias constraints to the average of the FLASK mocks using either FLASK (DES-Y1 run) or CosmoLike (quick run) covariance matrices with physical scale cuts
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