Systematic Bias in Cosmic Shear: Beyond the Fisher Matrix

TL;DR

This paper introduces an extension to the Fisher matrix formalism to accurately compute biases in cosmological parameters caused by systematic signals in weak lensing measurements, emphasizing the importance of detailed systematic modeling.

Contribution

We develop a method to quantify systematic biases in parameter estimation beyond the Fisher matrix, applied to weak lensing systematics with practical survey implications.

Findings

Residual systematics must be tightly controlled to avoid biasing cosmological parameters.

Redshift dependence of systematics significantly affects bias estimates.

Specific calibration accuracy thresholds are identified for future surveys like DUNE.

Abstract

We describe a method for computing the biases that systematic signals introduce in parameter estimation using a simple extension of the Fisher matrix formalism. This allows us to calculate the offset of the best fit parameters relative to the fiducial model, in addition to the usual statistical error ellipse. As an application, we study the impact that residual systematics in tomographic weak lensing measurements. In particular we explore three different types of shape measurement systematics: (i) additive systematic with no redshift evolution; (ii) additive systematic with redshift evolution; and (iii) multiplicative systematic. In each case, we consider a wide range of scale dependence and redshift evolution of the systematics signal. For a future DUNE-like full sky survey, we find that, for cases with mild redshift evolution, the variance of the additive systematic signal should be kept below 10^-7 to ensure biases on cosmological parameters that are sub-dominant to the statistical errors. For the multiplicative systematics, which depends on the lensing signal, we find the multiplicative calibration m0 needs to be controlled to an accuracy better than 10^-3. We find that the impact of systematics can be underestimated if their assumes redshift dependence is too simplistic. We provide simple scaling relations to extend these requirements to any survey geometry and discuss the impact of our results for current and future weak lensing surveys.