Perturbative approach to covariance matrix of the matter power spectrum

Abstract

We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (beat coupling or super-sample variance), and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10\% level up to $k\sim 1h\mathrm{Mp}{\mathrm{c}}^{-1}$. We show that all the connected components are dominated by the large-scale modes ($k<0.1h\mathrm{Mp}{\mathrm{c}}^{-1}$), regardless of the value of the wavevectors $k,k^{\prime }$ of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher $k$ it is dominated by a single eigenmode. The full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally, we provide a prescription for how to evaluate the covariance matrix from small box simulations without the need to simulate large volumes.

22 pages, 17 figures, 1 table

References in corpus (12)

• Cosmology and the Bispectrum
• Separate Universe Simulations
• Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum
• Probing dark energy with cluster counts and cosmic shear power spectra: including the full covariance
• Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum
• Analytic model for the matter power spectrum, its covariance matrix, and baryonic effects
• Super-Sample Signal
• Matter Power Spectrum Covariance Matrix from the DEUS-PUR ΛCDM simulations: Mass Resolution and non-Gaussian Errors
• Halo Zeldovich model and perturbation theory: dark matter power spectrum and correlation function
• Simulations of Baryon Acoustic Oscillations I: Growth of Large-Scale Density Fluctuations
• Joint likelihood function of cluster counts and $n$-point correlation functions: Improving their power through including halo sample variance
• Baryonic effects on weak-lensing two-point statistics and its cosmological implications

Cited by in corpus (25)

• Cosmological constraints from BOSS with analytic covariance matrices
• The cosmology dependence of galaxy clustering and lensing from a hybrid $N$-body-perturbation theory model
• Generating Log-normal Mock Catalog of Galaxies in Redshift Space
• Joint analysis of anisotropic power spectrum, bispectrum and trispectrum: application to N-body simulations
• Maximal compression of the redshift space galaxy power spectrum and bispectrum
• Matter trispectrum: theoretical modelling and comparison to N-body simulations
• The Effective Halo Model: Creating a Physical and Accurate Model of the Matter Power Spectrum and Cluster Counts
• Galaxy 2-Point Covariance Matrix Estimation for Next Generation Surveys
• Moving around the cosmological parameter space: a nonlinear power spectrum reconstruction based on high-resolution cosmic responses
• Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space
• Covariance of the matter power spectrum including the survey window function effect: N-body simulations vs. fifth-order perturbation theory on grid
• Perturbation theory for the redshift-space matter power spectra after reconstruction
• Covariance of the redshift-space matter power spectrum after reconstruction
• RSD measurements from BOSS galaxy power spectrum using the halo perturbation theory model
• Towards cosmological constraints from the compressed modal bispectrum: a robust comparison of real-space bispectrum estimators
• $\alpha$-attractor dark energy in view of next-generation cosmological surveys
• Bayesian Control Variates for optimal covariance estimation with pairs of simulations and surrogates
• The Uchuu-GLAM BOSS and eBOSS LRG lightcones: Exploring clustering and covariance errors
• Hitting the mark: Optimising Marked Power Spectra for Cosmology
• Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements
• A comparison of shrinkage estimators of the cosmological precision matrix
• Modelling the covariance matrix for the power spectra before and after the BAO reconstruction
• Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field $\mathrm{II}$: 1-Loop Corrections with Third-Order Densities
• Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field $\mathrm{I}$: 1-Loop Corrections involving Second-Order Densities
• Origin & evolution of the Universe