KiDS+VIKING-450: Improved cosmological parameter constraints from redshift calibration with self-organising maps

TL;DR

This study applies self-organising maps to recalibrate redshift distributions for the KV450 cosmic shear data, constructing robust 'gold' samples that align photometric sources with spectroscopic calibrators. By exploring multiple spectroscopic exclusions and priors (including non-zero mean redshift biases), the authors demonstrate that cosmological inferences, particularly S8, are stable against potential spectroscopic misrepresentation. The fiducial result, S8 ≈ 0.716, remains consistent with prior KV450 analyses, while variations in redshift priors and sample choices yield only small shifts, indicating reduced susceptibility to redshift calibration biases. The work also provides a generalized analysis pipeline (CosmoPipe/CosmoWrapper) and strengthens the conclusion that redshift calibration biases are unlikely to explain the Planck–KiDS tension, contributing to the reliability of weak-lensing cosmology.

Abstract

We present updated cosmological constraints for the KiDS+VIKING-450 cosmic shear data set (KV450), estimated using redshift distributions and photometric samples defined using self-organising maps (SOMs). Our fiducial analysis finds marginal posterior constraints of $S_8\equivσ_8\sqrt{Ω_{\rm m}/0.3}=0.716^{+0.043}_{-0.038}$; smaller than, but otherwise consistent with, previous work using this data set ($|ΔS_8| = 0.023$). We analyse additional samples and redshift distributions constructed in three ways: excluding certain spectroscopic surveys during redshift calibration, excluding lower-confidence spectroscopic redshifts in redshift calibration, and considering only photometric sources which are jointly calibrated by at least three spectroscopic surveys. In all cases, the method utilised here proves robust: we find a maximal deviation from our fiducial analysis of $|ΔS_8| \leq 0.011$ for all samples defined and analysed using our SOM. To demonstrate the reduction in systematic biases found within our analysis, we highlight our results when performing redshift calibration without the DEEP2 spectroscopic data set. In this case we find marginal posterior constraints of $S_8=0.707_{-0.042}^{+0.046}$; a difference with respect to the fiducial that is both significantly smaller than, and in the opposite direction to, the equivalent shift from previous work. These results suggest that our improved cosmological parameter estimates are insensitive to pathological misrepresentation of photometric sources by the spectroscopy used for direct redshift calibration, and therefore that this systematic effect cannot be responsible for the observed difference between $S_8$ estimates made with KV450 and Planck CMB probes.

Figures (3)

• Figure 1: Posterior constraints of $S_8$ (left) and $\Omega_{\rm m}$ vs. $S_8$ (right) for our various gold samples, compared to the results from hildebrandt/etal:2020 and Planck CMB. We show results for our analyses split into sections, determined by the form of their redshift distribution priors. Results computed using more informative, non-zero mean, Gaussian redshift distribution bias priors ('$\delta z\neq0$', see Appendix \ref{['app:\npriors']}) for gold samples where these are able to be calculated, and using the zero mean Gaussian bias priors from hildebrandt/etal:2020 otherwise ('$\delta z=0$'). For our fiducial analysis we show results with both priors, to allow direct comparison between our various results. We annotate our contour figure (right) with the two Gaussian smoothing kernels used in generating the contours (one for the cosmic shear contours, and one for the CMB contours). We find that our new cosmology pipeline produces results consistent with the pipeline of hildebrandt/etal:2020 (left panel, blue dashed box). Our fiducial results (orange) suggest a slightly lower $S_8$ than found in previous work: $S_8=0.716_{-0.038}^{+0.043}$. However we find that constraints on $S_8$ are extremely stable for all of our gold sample analyses here (compared to the fiducial: $|\Delta S_8|<0.2\sigma$), demonstrating that the results here are more robust to spectroscopic misrepresentation than previous works. In particular, unlike hildebrandt/etal:2020, we find that even pathological misrepresentation at high-redshift ('noDEEP2') is unable to shift our estimates of $S_8$ to larger values.
• Figure 2: Marginal posterior distributions for a subset of the cosmological, nuisance, and derived parameters used in our cosmological model. Coloured lines represent the marginal distributions from various samples. Dashed lines show the priors for all non-derived parameters. There is a clear difference between the marginal distributions of the gold and full-sample ('KV450-DIR') analyses. We note in particular that the previously observed preference within KV450 for small values of the matter density parameter $\Omega_{\rm m}$ is removed in our gold analyses. The gold analyses also prefer a lower value of $A_{\rm IA}$, consistent with $0$ in all cases.
• Figure 3: Marginal and 2D posterior distributions for a subset of the cosmological, nuisance, and derived parameters used in our cosmological model. We restrict this figure to only the 'KV450-DIR $\delta z$' (purple), 'SOM-Gold Fidicial $\delta z$' (gold), and 'SOM-Gold noDEEP2 $\delta z$' (green) analyses, as these three analyses encompase the range of posteriors in all of our gold sample analyses (and show similar degeneracies). The joint posterior of $A_{\rm IA}$ and $S_8$ demonstrates that, were a stronger prior on $A_{\rm IA}$ justifiable, agreement between the various gold samples would be even higher.