Thinking Outside the Box: Effects of Modes Larger than the Survey on Matter Power Spectrum Covariance

Abstract

Considering the matter power spectrum covariance matrix, it has recently been found that there is a potentially dominant effect on mildly non-linear scales due to power in modes of size equal to and larger than the survey volume. This {\it beat coupling} effect has been derived analytically in perturbation theory and while it has been tested with simulations, some questions remain unanswered. Moreover, there is an additional effect of these large modes, which has so far not been included in analytic studies, namely the effect on the estimated {\it average} density which enters the power spectrum estimate. In this article, we work out analytic, perturbation theory based expressions including both the beat coupling and this {\it local average effect} and we show that while, when isolated, beat coupling indeed causes large excess covariance in agreement with the literature, in a realistic scenario this is compensated almost entirely by the local average effect, leaving only $\sim 10$ of the excess. We test our analytic expressions by comparison to a suite of large N-body simulations. For the variances, we find excellent agreement with the analytic expressions for $k<0.2h$Mpc${}^{-1}$ at $z=0.5$, while the correlation coefficients agree to beyond $k=0.4h$Mpc${}^{-1}$. As expected, the range of agreement increases towards higher redshift and decreases slightly towards $z=0$. We finish by including the large-mode effects in a full covariance matrix description for arbitrary survey geometry and confirming its validity using simulations. This may be useful as a stepping stone towards building an actual galaxy (or other tracer's) power spectrum covariance matrix. [abridged]

24 pages, 10 figures. Version accepted for publication in JCAP. Added Figure 5 and Appendix A

References in corpus (8)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations
• Cosmology and the Bispectrum
• Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum
• Information content in the halo-model dark-matter power spectrum
• Luminous Red Galaxy Halo Density Field Reconstruction and Application to Large Scale Structure Measurements
• Removable Matter-Power-Spectrum Covariance from Bias Fluctuations

Cited by in corpus (62)

• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the Quasar Sample in configuration space between redshift 0.8 and 2.2
• Power Spectrum Super-Sample Covariance
• Super-Sample Covariance in Simulations
• Gaussian covariance matrices for anisotropic galaxy clustering measurements
• KiDS-1000 Methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis
• Information content of weak lensing power spectrum and bispectrum: including the non-Gaussian error covariance matrix
• Galaxy Power Spectrum Multipoles Covariance in Perturbation Theory
• Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum
• Cosmological constraints from BOSS with analytic covariance matrices
• Assessment of the Information Content of the Power Spectrum and Bispectrum
• An improved fitting formula for the dark matter bispectrum
• Measurement of Parity-Odd Modes in the Large-Scale 4-Point Correlation Function of SDSS BOSS DR12 CMASS and LOWZ Galaxies
• Super-Sample Signal
• Cosmological perturbation theory in 1+1 dimensions
• Comparing approximate methods for mock catalogues and covariance matrices III: Bispectrum
• Simulations of Weak Gravitational Lensing - II : Including Finite Support Effects in Cosmic Shear Covariance Matrices
• Improving fast generation of halo catalogs with higher-order Lagrangian perturbation theory
• Cosmological constraints from the power spectrum of eBOSS emission line galaxies
• Accurate cosmic shear errors: do we need ensembles of simulations?
• Complete super-sample lensing covariance in the response approach
• Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space
• On the impact of galaxy bias uncertainties on primordial non-Gaussianity constraints
• Generating Log-normal Mock Catalog of Galaxies in Redshift Space
• Perturbative approach to covariance matrix of the matter power spectrum
• Joint analysis of anisotropic power spectrum, bispectrum and trispectrum: application to N-body simulations
• Improving the precision matrix for precision cosmology
• Galaxy power-spectrum responses and redshift-space super-sample effect
• Large Covariance Matrices: Smooth Models from the 2-Point Correlation Function
• Bispectrum Supersample Covariance
• The impact of large-scale tides on cosmological distortions via redshift-space power spectrum
• Galaxy 2-Point Covariance Matrix Estimation for Next Generation Surveys
• Estimating the power spectrum covariance matrix with fewer mock samples
• Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space
• Analytic Gaussian Covariance Matrices for Galaxy $N$-Point Correlation Functions
• Precision cosmology in muddy waters: Cosmological constraints and N-body codes
• On the information content of the matter power spectrum
• Estimating sparse precision matrices
• SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition
• An optimal survey geometry of weak lensing survey: minimizing super-sample covariance
• Covariance of the matter power spectrum including the survey window function effect: N-body simulations vs. fifth-order perturbation theory on grid
• Local Primordial Non-Gaussianities and Super-Sample Variance
• Lagrangian approach to super-sample effects on biased tracers at field level: galaxy density fields and intrinsic alignments
• Covariances for cosmic shear and galaxy-galaxy lensing in the response approach
• Super-sample covariance of the power spectrum, bispectrum, halos, voids, and their cross covariances
• The Manhattan Suite: Accelerated galaxy evolution in the early Universe
• Indra: a Public Computationally Accessible Suite of Cosmological $N$-body Simulations
• Optimal Weights For Measuring Redshift Space Distortions in Multi-tracer Galaxy Catalogues
• Super-sample tidal modes on the celestial sphere
• On fast Generation of Cosmological Random Fields
• Harmonic analysis of isotropic fields on the sphere with arbitrary masks
• Forecasting Super-Sample Covariance in Future Weak Lensing Surveys with SuperSCRAM
• Improving initialization and evolution accuracy of cosmological neutrino simulations
• Keeping It Real: Revisiting a Real-Space Approach to Running Ensembles of Cosmological N-body Simulations
• What is the super-sample covariance? A fresh perspective for second-order shear statistics
• Impact of our local environment on cosmological statistics
• The impact of super-survey modes on cosmological constraints from cosmic shear fields
• Separating Angular and Radial Modes with Spherical-Fourier Bessel Power Spectrum on All Scales and Implications for Systematics Mitigation
• Breaking degeneracies with the Sunyaev-Zeldovich full bispectrum
• An Optimally Weighted Estimator of the Linear Power Spectrum Disentangling the Growth of Density Perturbations Across Galaxy Surveys
• Modelling the covariance matrix for the power spectra before and after the BAO reconstruction
• Super sample covariance and the volume scaling of galaxy survey covariance matrices
• An empirical nonlinear power spectrum overdensity-response