Simulating the Effect of Non-Linear Mode-Coupling in Cosmological Parameter Estimation

Abstract

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Euclid-like survey. In both cases we find that the 68% confidence area of the Omega_m-sigma_8 plane increases by a factor 5. However, the marginal errors increase by just 20 to 40%. We propose a new method to model the effects of nonlinear shear-power mode-coupling in the Fisher Matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68% confidence regions of the full Maximum Likelihood analysis in the Omega_m-sigma_8 plane to high accuracy for both 2-D and tomographic weak lensing surveys. Finally, we perform a multi-parameter analysis of Omega_m, sigma_8, h, n_s, w_0 and w_a to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. (Abridged)

Submitted to MNRAS. 11 pages, 8 figures

References in corpus (7)

• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Figure of Merit for Dark Energy Constraints from Current Observational Data
• Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum
• Cosmic variance of weak lensing surveys in the non-Gaussian regime
• Information content in the halo-model dark-matter power spectrum
• SUNGLASS: A new weak lensing simulation pipeline
• Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak Lensing Analysis

Cited by in corpus (13)

• Putting the Precision in Precision Cosmology: How accurate should your data covariance matrix be?
• Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure
• Gravitational Lensing Simulations I : Covariance Matrices and Halo Catalogues
• Joint analysis of cluster number counts and weak lensing power spectrum to correct for the super-sample covariance
• Matter Power Spectrum Covariance Matrix from the DEUS-PUR ΛCDM simulations: Mass Resolution and non-Gaussian Errors
• Impact of the non-Gaussian covariance of the weak lensing power spectrum and bispectrum on cosmological parameter estimation
• SKA Weak Lensing III: Added Value of Multi-Wavelength Synergies for the Mitigation of Systematics
• Response Approach to the Matter Power Spectrum Covariance
• Ringing the initial Universe: the response of overdensity and transformed-density power spectra to initial spikes
• The impact of baryons on the sensitivity of dark energy measurements
• Using Cross-Correlations to Calibrate Lensing Source Redshift Distributions: Improving Cosmological Constraints from Upcoming Weak Lensing Surveys
• Fast generation of weak lensing maps by the inverse-Gaussianization method
• Towards determining the neutrino mass hierarchy: weak lensing and galaxy clustering forecasts with baryons and intrinsic alignments