Efficient computation of the super-sample covariance for stage IV galaxy surveys

TL;DR

This paper introduces an efficient formula for the inverse super-sample covariance matrix, enabling faster and more reliable cosmological analyses for stage IV galaxy surveys, and assesses the impact of modeling inaccuracies on constraints.

Contribution

It presents a novel, computationally efficient framework for calculating super-sample covariance and demonstrates its application in cosmological parameter estimation.

Findings

Weak-lensing analysis is highly sensitive to response scale dependence, requiring 15% calibration.

Joint weak-lensing and galaxy clustering analysis is less sensitive, needing calibration better than 30%.

The proposed formula improves speed, stability, and ease of implementation in cosmological pipelines.

Abstract

Super-sample covariance (SSC) is an important effect for cosmological analyses that use the deep structure of the cosmic web; it may, however, be nontrivial to include it practically in a pipeline. We solve this difficulty by presenting a formula for the precision (inverse covariance) matrix and show applications to update likelihood or Fisher forecast pipelines. The formula has several advantages in terms of speed, reliability, stability, and ease of implementation. We present an analytical application to show the formal equivalence between three approaches to SSC: (i) at the usual covariance level, (ii) at the likelihood level, and (iii) with a quadratic estimator. We then present an application of this computationally efficient framework for studying the impact of inaccurate modelling of SSC responses for cosmological constraints from stage IV surveys. We find that a weak-lensing-only analysis is very sensitive to inaccurate modelling of the scale dependence of the response, which needs to be calibrated at the $\sim15\%$ level. The sensitivity to this scale dependence is less severe for the joint weak-lensing and galaxy clustering analysis (also known as 3x2pt). Nevertheless, we find that both the amplitude and scale-dependence of the responses have to be calibrated at better than 30\%.