Gaussianizing the non-Gaussian lensing convergence field I: the performance of the Gaussianization

Abstract

Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010, we proposed a Gaussianization transform to Gaussianize the non-Gaussian lensing convergence field $\kappa$. It performs a local monotonic transformation $\kappa \to y$ pixel by pixel to make the unsmoothed one-point probability distribution function of the new variable $y$ Gaussian. We tested whether the whole $y$ field is Gaussian against N-body simulations. (1) We found that the proposed Gaussianization suppresses the non-Gaussianity by orders of magnitude, in measures of the skewness, the kurtosis, the 5th- and 6th-order cumulants of the $y$ field smoothed over various angular scales relative to that of the corresponding smoothed $\kappa$ field. The residual non-Gaussianities are often consistent with zero within the statistical errors. (2) The Gaussianization significantly suppresses the bispectrum. Furthermore, the residual scatters around zero, depending on the configuration in the Fourier space. (3) The Gaussianization works with even better performance for the 2D fields of the matter density projected over $\sim 300 \mpch$ distance interval centered at $z\in (0,2)$, which can be reconstructed from the weak lensing tomography. (4) We identified imperfectness and complexities of the proposed Gaussianization. We noticed weak residual non-Gaussianity in the $y$ field. We verified the widely used logarithmic transformation as a good approximation to the Gaussianization transformation. However, we also found noticeable deviations.

13 pages, 15 figures, accepted by PRD

References in corpus (31)

• The cosmological simulation code GADGET-2
• Weak Gravitational Lensing
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Weak Gravitational Lensing by Large-Scale Structure
• Weak Gravitational Lensing and its Cosmological Applications
• Cosmological parameters from lensing power spectrum and bispectrum tomography
• Dark matter maps reveal cosmic scaffolding
• The Skewness of the Aperture Mass Statistic
• Cosmology with Weak Lensing Surveys
• Correcting for the alias effect when measuring the power spectrum using FFT
• The Impact of Non-Gaussian Errors on Weak Lensing Surveys
• Rejuvenating the matter power spectrum: restoring information with a logarithmic density mapping
• Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications
• Information content of the non-linear matter power spectrum
• Detection of non-Gaussian Signatures in the VIRMOS-DESCART Lensing Survey
• Detection of dark matter Skewness in the VIRMOS-DESCART survey: Implications for Ω_0
• Weighing the Cosmological Energy Contents with Weak Gravitational Lensing
• Information content of the non-linear power spectrum: the effect of beat-coupling to large scales
• Cosmic variance of weak lensing surveys in the non-Gaussian regime
• The Weak Lensing Bispectrum
• Rejuvenating Power Spectra II: the Gaussianized galaxy density field
• Re-capturing cosmic information
• Non-Gaussianity and the recovery of the mass power spectrum from the Ly$\alpha$ forest
• Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak Lensing Analysis
• Weak Lensing Statistics as a Probe of Omega and Power Spectrum
• Copula Cosmology: Constructing a Likelihood Function
• From Finance to Cosmology: The Copula of Large-Scale Structure
• Precise Estimation of Cosmological Parameters Using a More Accurate Likelihood Function
• Second Order Geodesic Corrections to Cosmic Shear
• Increasing the Fisher Information Content in the Matter Power Spectrum by Non-linear Wavelet Weiner Filtering
• Nonlinearities in modified gravity cosmology I: signatures of modified gravity in the nonlinear matter power spectrum

Cited by in corpus (25)

• The Initial Conditions of the Universe from Constrained Simulations
• Cosmic shear covariance: The log-normal approximation
• Galaxy and Mass Assembly (GAMA): Redshift Space Distortions from the Clipped Galaxy Field
• On the inadequacy of N-point correlation functions to describe nonlinear cosmological fields: explicit examples and connection to simulations
• Cosmological information in Gaussianised weak lensing signals
• Optimal non-linear transformations for large scale structure statistics
• Rejuvenating the Matter Power Spectrum III: The Cosmology Sensitivity of Gaussianized Power Spectra
• Ringing the initial Universe: the response of overdensity and transformed-density power spectra to initial spikes
• One-point remapping of Lagrangian perturbation theory in the mildly non-linear regime of cosmic structure formation
• Sufficient observables for large scale structure in galaxy surveys
• The Clustering of Galaxies in the Completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmic Flows and Cosmic Web from Luminous Red Galaxies
• Dark Energy from the log-transformed convergence field
• Tomography and Weak lensing Statistics
• On the total cosmological information in galaxy clustering: an analytical approach
• Fast generation of weak lensing maps by the inverse-Gaussianization method
• Gaussianizing the non-Gaussian lensing convergence field II: the applicability to noisy data
• One-point statistics of the Lagrangian displacement field
• The copula of the cosmological matter density field is non-Gaussian
• The Weak Lensing Peak Statistics in the Mocks by the inverse-Gaussianization Method
• A possible explanation of vanishing halo velocity bias
• Optimizing the Recovery of Fisher Information in the Dark Matter Power Spectrum
• Numerical investigation of non-Gaussianities in the phase and modulus of density Fourier modes
• Neural style transfer of weak lensing mass maps
• About One-point Statistics of the Ratio of Two Fourier-transformed Cosmic Fields and an Application
• Modification of Newtonian Gravity: Implications for Hot Gas in Clusters and Galactic Angular Momentum