The impact of super-survey modes on cosmological constraints from cosmic shear fields

TL;DR

This paper investigates how super-survey modes, affected by the mass-sheet degeneracy, limit the cosmological information extractable from cosmic shear fields, showing that most information is lost without additional data.

Contribution

It quantifies the impact of super-survey modes on cosmological constraints using a lognormal model and demonstrates the severe information loss inherent in shear-based observables.

Findings

Super-survey modes cause significant information loss in cosmic shear analyses.

Reconstructing background modes increases information content by a factor of two.

Typically, 80-90% of information is lost below angular scale  3000 without extra data.

Abstract

Owing to the mass-sheet degeneracy, cosmic shear maps do not probe directly the Fourier modes of the underlying mass distribution on scales comparable to the survey size and larger. To assess the corresponding effect on attainable cosmological parameter constraints, we quantify the information on super-survey modes in a lognormal model and, when interpreted as nuisance parameters, their degeneracies to cosmological parameters. Our analytical and numerical calculations clarify the central role of super-sample covariance (SSC) in shaping the statistical power of cosmological observables. Reconstructing the background modes from their non-Gaussian statistical dependence to small scales modes yields the renormalized convergence. This diagonalizes the spectrum covariance matrix, and the information content of the corresponding power spectrum is increased by a factor of two over standard methods. Unfortunately, careful calculation of the Cramer-Rao bound shows that the information recovery can never be made complete, any observable built from shear fields, including optimal sufficient statistics, are subject to severe information loss, typically $80\%$ to $90\%$ below $\ell \sim 3000$ for generic cosmological parameters. The lost information can only be recovered from additional, non-shear based data. Our predictions hold just as well for a tomographic analysis, and/or full sky surveys.