Power Spectrum Super-Sample Covariance

TL;DR

This paper presents a unified approach to understanding super-sample covariance's impact on power spectrum estimation, linking it to the matter trispectrum and background density response, applicable across various survey types.

Contribution

It introduces a unified framework connecting super-sample covariance effects to the matter trispectrum and background density response, applicable to multiple statistical measures.

Findings

Super-sample covariance dominates small-scale power spectrum variance.

The matter trispectrum in squeezed configurations underpins the covariance.

The approach enables calibration from simulations and views covariance as a signal.

Abstract

We provide a simple, unified approach to describing the impact of super-sample covariance, or beat coupling, on power spectrum estimation in a finite-volume survey. For a wide range of survey volumes, the sample variance that arises from modes that are larger than the survey dominates the covariance of power spectrum estimators for modes much smaller than the survey. The deeply nonlinear version of this effect is known as halo sample variance. We show that all variants are unified by the matter trispectrum of squeezed configurations and that such configurations obey a consistency relation which relates them to the response of the power spectrum to a change in the background density. Our method also applies to statistics that are based on radial projections of the density field such as weak lensing shear. While we use the halo model for an analytic description to expose the nature of the effect, the consistency description enables an accurate calibration of the full effect directly from simulations. It also suggests that super-sample covariance may be viewed as an additional interesting signal rather than excess noise.