Simultaneous Constraints on Cosmology and Photometric Redshift Bias from Weak Lensing and Galaxy Clustering

TL;DR

This paper explores how combining weak lensing and galaxy clustering data can constrain cosmology while mitigating redshift bias errors through marginalization and self-calibration techniques.

Contribution

It demonstrates that joint analysis and marginalization over redshift biases can effectively reduce systematic errors in cosmological parameter estimation.

Findings

Redshift bias of 0.05 causes >2σ bias in key parameters.

Marginalizing over biases retains most cosmological information.

Self-calibration effectiveness varies with experiment specifics.

Abstract

We investigate the expected cosmological constraints from a combination of weak lensing and large-scale galaxy clustering using realistic redshift distributions. Introducing a systematic bias in the weak lensing redshift distributions (of 0.05 in redshift) produces a $>2\sigma$ bias in the recovered matter power spectrum amplitude and dark energy equation of state, for preliminary Stage III surveys. We demonstrate that these cosmological errors can be largely removed by marginalising over unknown biases in the assumed weak lensing redshift distributions, if we assume high quality redshift information for the galaxy clustering sample. Furthermore the cosmological constraining power is mostly retained despite removing much of the information on the weak lensing redshift distribution biases. We show that this comes from complementary degeneracy directions between cosmic shear and the combination of galaxy clustering with cross-correlation between shear and galaxy number density. Finally we examine how the self-calibration performs when the assumed distributions differ from the true distributions by more than a simple uniform bias. We find that the effectiveness of this self-calibration method will depend on the details of a given experiment and the nature of the uncertainties on the estimated redshift distributions.