Analytic marginalization of $N(z)$ uncertainties in tomographic galaxy surveys

TL;DR

This paper introduces an analytical method to marginalize over uncertainties in redshift distributions in galaxy surveys, improving the robustness of cosmological parameter estimation by effectively downweighting sensitive data modes.

Contribution

The authors develop a linear expansion approach that allows for analytical marginalization over complex $N(z)$ uncertainties, applicable to large parameter spaces in photometric galaxy surveys.

Findings

Method successfully applied to Hyper Suprime-Cam data

Effectively marginalizes over calibration sample variance

Reduces sensitivity to systematic uncertainties in $N(z)$

Abstract

We present a new method to marginalize over uncertainties in redshift distributions, $N(z)$, within tomographic cosmological analyses applicable to current and upcoming photometric galaxy surveys. We allow for arbitrary deviations from the best-guess $N(z)$ governed by a general covariance matrix describing the uncertainty in our knowledge of redshift distributions. In principle, this is marginalization over hundreds or thousands of new parameters describing potential deviations as a function of redshift and tomographic bin. However, by linearly expanding the theory predictions around a fiducial model, this marginalization can be performed analytically, resulting in a modified data covariance matrix that effectively downweights the modes of the data vector that are more sensitive to redshift distribution variations. We showcase this method by applying it to the galaxy clustering measurements from the Hyper Suprime-Cam first data release. We illustrate how to marginalize over sample-variance of the calibration sample and a large general systematic uncertainty in photometric estimation methods, and explore the impact of priors imposing smoothness in the redshift distributions.