KiDS+VIKING-450 cosmology with Bayesian hierarchical model redshift distributions

TL;DR

This paper applies a Bayesian hierarchical model to KiDS+VIKING-450 weak lensing data to improve redshift distribution estimates, reducing tension with Planck cosmology and refining matter density measurements.

Contribution

It demonstrates the application of a Bayesian hierarchical framework to infer galaxy redshift distributions in weak lensing data, improving cosmological parameter constraints.

Findings

Bayesian method increases the clustering parameter S8, reducing tension with Planck.

Redshift distribution inference is robust to subset selection, with subdominant impact on cosmology.

The inferred matter density Omega_m is 0.31 ± 0.10.

Abstract

Tomographic redshift distributions from photometric data are crucial ingredients in cosmic shear analysis, since they are required for the theoretical calculation of the signal based on the redshift distribution of the galaxies where the shear field is sampled. In this paper, we develop as a proof of concept Leistedt et al.'s template-based Bayesian Hierarchical Model framework into an application to weak lensing data by sampling the redshift distributions of the galaxies in the KiDS+VIKING-450 survey. We also use a principal component analysis to provide a set of representative templates drawn from a large superset. For computational tractability, subsets of $10^5$ galaxies are chosen to determine the redshift distributions, and we test the sensitivity of the cosmological inference to the subset chosen, finding it to be subdominant compared to the statistical error. We marginalise over the inferred redshift distributions and find that the Bayesian method increases the clustering parameter compared with previous studies, alleviating the $S_8$ tension with Planck, where $S_{8}\equiv\sigma_{8}\sqrt{\Omega_{\tm{m}}/0.3}=0.756\pm 0.039$, assuming flat $\Lambda$CDM. The tension with Planck for this survey is reduced from $2.3\sigma$ to $1.9\sigma$. We also infer a value for the matter density, $\Omega_{\tm{m}}=0.31\pm 0.10$.