Non-Gaussian Error Contribution to Likelihood Analysis of the Matter Power Spectrum

Abstract

We study the sample variance of the matter power spectrum for the standard Lambda Cold Dark Matter universe. We use a total of 5000 cosmological N-body simulations to study in detail the distribution of best-fit cosmological parameters and the baryon acoustic peak positions. The obtained distribution is compared with the results from the Fisher matrix analysis with and without including non-Gaussian errors. For the Fisher matrix analysis, we compute the derivatives of the matter power spectrum with respect to cosmological parameters using directly full nonlinear simulations. We show that the non-Gaussian errors increase the unmarginalized errors by up to a factor 5 for k_{max}=0.4h/Mpc if there is only one free parameter provided other parameters are well determined by external information. On the other hand, for multi-parameter fitting, the impact of the non-Gaussian errors is significantly mitigated due to severe parameter degeneracies in the power spectrum. The distribution of the acoustic peak positions is well described by a Gaussian distribution, with its width being consistent with the statistical interval predicted from the Fisher matrix. We also examine systematic bias in the best-fit parameter due to the non-Gaussian errors. The bias is found to be smaller than the 1 sigma statistical error for both the cosmological parameters and the acoustic scale positions.

arXiv comment12 pages, 10 figures, accepted for publication in ApJ, minor changes

References in corpus (80)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• The cosmological simulation code GADGET-2
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Efficient Computation of CMB anisotropies in closed FRW models
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications
• Stable clustering, the halo model and nonlinear cosmological power spectra
• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample
• GADGET: A code for collisionless and gasdynamical cosmological simulations
• Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
• Power Spectrum Analysis of Three-Dimensional Redshift Surveys
• Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS
• Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys
• Clustering of Luminous Red Galaxies IV: Baryon Acoustic Peak in the Line-of-Sight Direction and a Direct Measurement of H(z)
• Renormalized Cosmological Perturbation Theory
• Probing dark energy using baryonic oscillations in the galaxy power spectrum as a cosmological ruler
• Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies
• Nonlinear Evolution of Baryon Acoustic Oscillations
• The Coyote Universe I: Precision Determination of the Nonlinear Matter Power Spectrum
• Cosmology and the Bispectrum
• Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture
• Cosmic Complementarity: H_0 and Omega_m from Combining CMB Experiments and Redshift Surveys
• Baryonic Signatures in Large-Scale Structure
• The Scale Dependence of Halo and Galaxy Bias: Effects in Real Space
• Power Spectrum Correlations Induced by Non-Linear Clustering
• The Baryonic Acoustic Feature and Large-Scale Clustering in the SDSS LRG Sample
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Baryonic acoustic oscillations in simulated galaxy redshift surveys
• Large-Scale Anisotropic Correlation Function of SDSS Luminous Red Galaxies
• Power Spectrum Covariance of Weak Gravitational Lensing
• Perturbation Theory Reloaded: Analytical Calculation of Non-linearity in Baryonic Oscillations in the Real Space Matter Power Spectrum
• Resumming Cosmic Perturbations
• The detectability of baryonic acoustic oscillations in future galaxy surveys
• Calibrating the Nonlinear Matter Power Spectrum: Requirements for Future Weak Lensing Surveys
• The Impact of Non-Gaussian Errors on Weak Lensing Surveys
• Simulations of Wide-Field Weak Lensing Surveys I: Basic Statistics and Non-Gaussian Effects
• A Closure Theory for Non-linear Evolution of Cosmological Power Spectra
• Rejuvenating the matter power spectrum: restoring information with a logarithmic density mapping
• Correlation Function in Deep Redshift Space as a Cosmological Probe
• Non-linear structure formation and the acoustic scale
• On measuring the covariance matrix of the nonlinear power spectrum from simulations
• The Growth of Correlations in the Matter Power Spectrum
• Non-linear Evolution of Baryon Acoustic Oscillations from Improved Perturbation Theory in Real and Redshift Spaces
• Cosmological parameter constraints from SDSS luminous red galaxies: a new treatment of large-scale clustering
• High-precision predictions for the acoustic scale in the non-linear regime
• Dark matter clustering: a simple renormalization group approach
• Modeling Nonlinear Evolution of Baryon Acoustic Oscillations: Convergence Regime of N-body Simulations and Analytic Models
• Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum
• Constraining Anisotropic Baryon Oscillations
• Information content of the non-linear matter power spectrum
• Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation
• Nonlinear power spectrum in the presence of massive neutrinos: perturbation theory approach, galaxy bias and parameter forecasts
• The Horizon Run N-body Simulation: Baryon Acoustic Oscillations and Topology of Large Scale Structure of the Universe
• Perturbation Theory Reloaded II: Non-linear Bias, Baryon Acoustic Oscillations and Millennium Simulation In Real Space
• Bispectrum and Nonlinear Biasing of Galaxies: Perturbation Analysis, Numerical Simulation and SDSS Galaxy Clustering
• Simulations of Baryon Oscillations
• Covariance of cross-correlations: towards efficient measures for large-scale structure
• Information content of the non-linear power spectrum: the effect of beat-coupling to large scales
• Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe
• Constraints on Neutrino Masses from Weak Lensing
• Extracting Angular Diameter Distance and Expansion Rate of the Universe from Two-dimensional Galaxy Power Spectrum at High Redshifts: Baryon Acoustic Oscillation Fitting versus Full Modeling
• Baryonic Acoustic Oscillations via the Renormalization Group
• Information content in the halo-model dark-matter power spectrum
• The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?
• Systematic effects in the sound horizon scale measurements
• What is the best way to measure baryonic acoustic oscillations?
• Information content in the halo-model dark-matter power spectrum II: Multiple cosmological parameters
• Simulations of Baryon Acoustic Oscillations I: Growth of Large-Scale Density Fluctuations
• Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak Lensing Analysis
• Deconstructing Baryon Acoustic Oscillations: A Comparison of Methods
• Moduli Corrections to D-term Inflation
• A fitting formula for the non-Gaussian contribution to the lensing power spectrum covariance
• Dark Energy from Large-Scale Structure Lensing Information
• A new model for the full shape of the large-scale power spectrum
• Baryon oscillations in galaxy and matter power-spectrum covariance matrices
• Damping of the baryon acoustic oscillations in the matter power spectrum as a probe of the growth factor
• The Non-Linear Fisher Information content of cosmic shear surveys

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