Variations of cosmic large-scale structure covariance matrices across parameter space

Abstract

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the nonlinear evolution of the cosmic web. As nonlinear clustering to date has only been described by numerical $N$-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work we describe the change of the matter covariance and of the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from nonlinear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to $\ell \le 1300$. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimising interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

10 pages, 6 figures, submitted to MNRAS

References in corpus (5)

• Parameter inference with estimated covariance matrices
• The onion universe: all sky lightcone simulations in spherical shells
• Probing dark energy with cluster counts and cosmic shear power spectra: including the full covariance
• Sample variance in weak lensing: how many simulations are required?
• Describing variations of the Fisher-matrix across parameter space

Cited by in corpus (12)

• KiDS+VIKING-450: Cosmic shear tomography with optical+infrared data
• Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space
• Massive data compression for parameter-dependent covariance matrices
• KiDS+GAMA: Constraints on Horndeski gravity from combined large-scale structure probes
• Cosmic Shear Covariance Matrix in $w$CDM: Cosmology Matters
• KiDS-SBI: Simulation-based inference analysis of KiDS-1000 cosmic shear
• Parameter constraints from weak lensing tomography of galaxy shapes and cosmic microwave background fluctuations
• Cosmological Model Parameter Dependence of the Matter Power Spectrum Covariance from the DEUS-PUR $Cosmo$ Simulations
• Cosmological Covariance of Fast Radio Burst Dispersions
• KiDS-Legacy: Covariance validation and the unified OneCovariance framework for projected large-scale structure observables
• Partition function approach to non-Gaussian likelihoods: Formalism and expansions for weakly non-Gaussian cosmological inference
• Origin & evolution of the Universe