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Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent withmore »the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

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Recent works have shown that weak lensing magnification must be included in upcoming large-scale structure analyses, such as for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), to avoid biasing the cosmological results. In this work, we investigate whether including magnification has a positive impact on the precision of the cosmological constraints, as well as being necessary to avoid bias. We forecast this using an LSST mock catalogue and a halo model to calculate the galaxy power spectra. We find that including magnification has little effect on the precision of the cosmological parameter constraints for an LSST galaxy clustering analysis, where the halo model parameters are additionally constrained by the galaxy luminosity function. In particular, we find that for the LSST gold sample (i < 25.3) including weak lensing magnification only improves the galaxy clustering constraint on Ωm by a factor of 1.03, and when using a very deep LSST mock sample (i < 26.5) by a factor of 1.3. Since magnification predominantly contributes to the clustering measurement and provides similar information to that of cosmic shear, this improvement would be reduced for a combined galaxy clustering and shear analysis. We also confirm that notmore »modelling weak lensing magnification will catastrophically bias the cosmological results from LSST. Magnification must therefore be included in LSST large-scale structure analyses even though it does not significantly enhance the precision of the cosmological constraints.

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We measured the cross-correlation between galaxy weak lensing data from the Kilo Degree Survey (KiDS-1000, DR4) and cosmic microwave background (CMB) lensing data from the Atacama Cosmology Telescope (ACT, DR4) and the Planck Legacy survey. We used two samples of source galaxies, selected with photometric redshifts, (0.1 <  z B  < 1.2) and (1.2 <  z B  < 2), which produce a combined detection significance of the CMB lensing and weak galaxy lensing cross-spectrum of 7.7 σ . With the lower redshift galaxy sample, for which the cross-correlation was detected at a significance of 5.3 σ , we present joint cosmological constraints on the matter density parameter, Ω m , and the matter fluctuation amplitude parameter, σ 8 , marginalising over three nuisance parameters that model our uncertainty in the redshift and shear calibration as well as the intrinsic alignment of galaxies. We find our measurement to be consistent with the best-fitting flat ΛCDM cosmological models from both Planck and KiDS-1000. We demonstrate the capacity of CMB weak lensing cross-correlations to set constraints on either the redshift or shear calibration by analysing a previously unused high-redshift KiDS galaxy sample (1.2 <  z B  < 2), with the cross-correlation detected at a significance of 7 σ .more »This analysis provides an independent assessment for the accuracy of redshift measurements in a regime that is challenging to calibrate directly owing to known incompleteness in spectroscopic surveys.« less

We investigate the sensitivity to the effects of lensing magnification on large-scale structure analyses combining photometric cosmic shear and galaxy clustering data (i.e. the now commonly called ‘3 × 2-point’ analysis). Using a Fisher matrix bias formalism, we disentangle the contribution to the bias on cosmological parameters caused by ignoring the effects of magnification in a theory fit from individual elements in the data vector, for Stage-III and Stage-IV surveys. We show that the removal of elements of the data vectors that are dominated by magnification does not guarantee a reduction in the cosmological bias due to the magnification signal, but can instead increase the sensitivity to magnification. We find that the most sensitive elements of the data vector come from the shear-clustering cross-correlations, particularly between the highest redshift shear bin and any lower redshift lens sample, and that the parameters ΩM, $S_8=\sigma _8\sqrt{\Omega _\mathrm{ M}/0.3}$, and w0 show the most significant biases for both survey models. Our forecasts predict that current analyses are not significantly biased by magnification, but this bias will become highly significant with the continued increase of statistical power in the near future. We therefore conclude that future surveys should measure and model the magnification as partmore »of their flagship ‘3 × 2-point’ analysis.

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