Intrinsic alignment (IA) modelling and photometric redshift estimation are two of the main sources of systematic uncertainty in weak lensing surveys. We investigate the impact of redshift errors and their interplay with different IA models. Generally, errors on the mean δz and on the width σz of the redshift bins can both lead to biases in cosmological constraints. We find that such biases can, however, only be partially resolved by marginalizing over δz   and σz . For Stage-III surveys, δz and σz cannot be well constrained due to limited statistics. The resulting biases are thus sensitive to prior volume effects. For Stage-IV surveys, we observe that marginalizing over the redshift parameters has an impact and reduces the bias. We derive requirements on the uncertainty of σz and δz for both Stage-III and Stage-IV surveys. We assume that the redshift systematic errors on S 8 should be less than half of the statistical errors, and the median bias should be smaller than 0.25σ. We find that the uncertainty on δz has to be ≲ 0.025 for the NLA IA model with a Stage-III survey. We find no requirement threshold for σz since the requirements are met even for our maximum prior width of 0.3. For the TATT IA model, the uncertainty on δz has to be ≲ 0.02 and the uncertainty on σz has to be ≲ 0.2. Current redshift precision of Stage-III surveys is therefore high enough to meet these requirements. For Stage-IV surveys, systematic effects will be more important due to the higher statistical precision. In this case, the uncertainty on δz has to be ≲ 0.005 and the uncertainty on σz should be ≲ 0.1, with no significant dependence on the IA model. This required high precision will be a challenge for the redshift calibration of these future surveys. Finally, we investigate whether the interplay between redshift systematics and IA modelling can explain the S 8-tension between cosmic shear results and CMB measurements. We find that this is unlikely to explain the current S 8-tension. The code that was used to conduct this analysis is publicly available.[refrigerator: https://cosmo-gitlab.phys.ethz.ch/cosmo_public/refrigerator.]

The next generation of weak lensing surveys will measure the matter distribution of the local Universe with unprecedented precision, allowing the resolution of non-Gaussian features of the convergence field. This encourages the use of higher-order mass-map statistics for cosmological parameter inference. We extend the forward-modelling based methodology introduced in a previous forecast paper to match these new requirements. We provide multiple forecasts for the wCDM parameter constraints that can be expected from stage 3 and 4 weak lensing surveys. We consider different survey setups, summary statistics and mass map filters including wavelets. We take into account the shear bias, photometric redshift uncertainties and intrinsic alignment. The impact of baryons is investigated and the necessary scale cuts are applied. We compare the angular power spectrum analysis to peak and minima counts as well as Minkowski functionals of the mass maps. We find a preference for Starlet over Gaussian filters. Our results suggest that using a survey setup with 10 instead of 5 tomographic redshift bins is beneficial. Adding cross-tomographic information improves the constraints on cosmology and especially on galaxy intrinsic alignment for all statistics. In terms of constraining power, we find the angular power spectrum and the peak counts to be equally matched for stage 4 surveys, followed by minima counts and the Minkowski functionals. Combining different summary statistics significantly improves the constraints and compensates the stringent scale cuts. We identify the most ‘cost-effective’ combination to be the angular power spectrum, peak counts and Minkowski functionals following Starlet filtering.

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