Response Approach to the Matter Power Spectrum Covariance

Abstract

We present a calculation of the matter power spectrum covariance matrix $\mathrm{Cov}({\mathbf{k}}_1,{\mathbf{k}}_2)$ that uses power spectrum responses to accurately describe the coupling between large- and small-scale modes beyond the perturbative regime. These response functions can be measured with (small-volume) N-body simulations, which is why the response contributions to the covariance remain valid and predictive at all orders in perturbation theory. A novel and key step presented here is the use of responses to compute loop contributions with soft loop momenta, which extends the application of the response approach beyond that of previously considered squeezed $n$-point functions. The calculation presented here does not involve any fitting parameters. When including response-type terms up to 1-loop order in perturbation theory, we find that our calculation captures the bulk of the total covariance as estimated from simulations up to values of $k_1,k_2\sim 1h/\mathrm{Mpc}$. Moreover, the prediction is guaranteed to be accurate whenever the softer mode is sufficiently linear, $\min \{k_1,k_2\}\lesssim 0.08h/\mathrm{Mpc}$. We identify and discuss straightforward improvements in the context of the response approach, which are expected to further increase the accuracy of the calculation presented here.

arXiv comment26 pages + appendices and references. 10 figures. Minor change in caption of Fig.3 in v2

References in corpus (52)

• Efficient Computation of CMB anisotropies in closed FRW models
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Properties of galaxies reproduced by a hydrodynamic simulation
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• The Effective Field Theorist's Approach to Gravitational Dynamics
• An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models
• Effects of Baryons and Dissipation on the Matter Power Spectrum
• Power Spectrum Super-Sample Covariance
• Power Spectrum Correlations Induced by Non-Linear Clustering
• The Coyote Universe Extended: Precision Emulation of the Matter Power Spectrum
• Putting the Precision in Precision Cosmology: How accurate should your data covariance matrix be?
• The Effect of Covariance Estimator Error on Cosmological Parameter Constraints
• Super-Sample Covariance in Simulations
• Simulations of Wide-Field Weak Lensing Surveys I: Basic Statistics and Non-Gaussian Effects
• Galaxy Bias and non-Linear Structure Formation in General Relativity
• Precision measurement of the local bias of dark matter halos
• Matter power spectrum and the challenge of percent accuracy
• On measuring the covariance matrix of the nonlinear power spectrum from simulations
• 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
• Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation
• The effect of baryons on redshift space distortions and cosmic density and velocity fields in the EAGLE simulation
• Analytic model for the matter power spectrum, its covariance matrix, and baryonic effects
• Self Calibration of Tomographic Weak Lensing for the Physics of Baryons to Constrain Dark Energy
• Super-Sample Signal
• On Separate Universes
• Non-Gaussian Covariance of the Matter Power Spectrum in the Effective Field Theory of Large Scale Structure
• The effect of relative velocity and density perturbations between baryons and dark matter on the clustering of galaxies
• Implementing the DC Mode in Cosmological Simulations with Supercomoving Variables
• Systematic Renormalization of the Effective Theory of Large Scale Structure
• The angle-averaged squeezed limit of nonlinear matter N-point functions
• Cosmic variance of weak lensing surveys in the non-Gaussian regime
• Large-scale assembly bias of dark matter halos
• Perturbative approach to covariance matrix of the matter power spectrum
• Responses in Large-Scale Structure
• Matter Power Spectrum Covariance Matrix from the DEUS-PUR ΛCDM simulations: Mass Resolution and non-Gaussian Errors
• Simulations of Wide-Field Weak Lensing Surveys II: Covariance Matrix of Real Space Correlation Functions
• Response function of the large-scale structure of the universe to the small scale inhomogeneities
• Large-scale tidal effect on redshift-space power spectrum in a finite-volume survey
• Ringing the initial Universe: the response of overdensity and transformed-density power spectra to initial spikes
• Non-Linear Matter Power Spectrum Covariance Matrix Errors and Cosmological Parameter Uncertainties
• On estimating cosmology-dependent covariance matrices
• Principal Shapes and Squeezed Limits in the Effective Field Theory of Large Scale Structure
• On the information content of the matter power spectrum
• Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-$\alpha$ forest power spectrum
• Removable Matter-Power-Spectrum Covariance from Bias Fluctuations
• Non-Gaussian Error in Galaxy Survey (Part 1)
• Effect of model-dependent covariance matrix for studying Baryon Acoustic Oscillations
• Large-Scale Tides in General Relativity
• Including parameter dependence in the data and covariance for cosmological inference
• Simulating the Effect of Non-Linear Mode-Coupling in Cosmological Parameter Estimation

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