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

¹ Dipartimento di Fisica e Astronomia “Galileo Galilei”, Universitá degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
² INFN, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
e-mail: fabien.lacasa@pd.infn.it
³ Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, 24 quai Ernest Ansermet, 1211 Geneva, Switzerland
⁴ Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405 Orsay, France
⁵ University of Lyon, UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, France
⁶ Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
⁷ Department of Physics and Trottier Space Institute, McGill University, Montreal, QC H3A2T8, Canada
⁸ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France

Received: 5 October 2022
Accepted: 11 January 2023

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 ∼15% level. The sensitivity to this scale dependence is less severe for the joint weak-lensing and galaxy clustering analysis (also known as 3×2pt). Nevertheless, we find that both the amplitude and scale-dependence of the responses have to be calibrated at better than 30%.