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

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 $\kappa\rightarrow y$ 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.Comment: 13 pages, 15 figures, accepted by PR

Recovering the Primordial Density Fluctuations: A comparison of methods

We present a comparative study of six different methods for reversing the gravitational evolution of a cosmological density field to recover the primordial fluctuations: linear theory, the Gaussianization mapping scheme, two different quasi-linear dynamical schemes based on the Zel'dovich approximation, a Hybrid dynamical-Gaussianization method and the Path Interchange Zel'dovich Approximation (PIZA). The final evolved density field from an N-body simulation constitutes our test case. We use a variety of statistical measures to compare the initial density field recovered from it to the true initial density field, using each of the six different schemes. These include point-by-point comparisons of the density fields in real space, the individual modes in Fourier space, as well as global statistical properties such as the genus, the PDF of the density, and the distribution of peak heights and their shapes. We find linear theory to be the most inaccurate of all the schemes. The Gaussianization scheme is the least accurate after linear theory. The two quasi-linear dynamical schemes are more accurate than Gaussianization, although they break down quite drastically when used outside their range of validity - the quasi-linear regime. The complementary beneficial aspects of the dynamical and the Gaussianization schemes are combined in the Hybrid method. We find this Hybrid scheme to be more accurate and robust than either Gaussianization or the dynamical method alone. The PIZA scheme performs substantially better than the others in all point-by-point comparisons. However, it produces an oversmoothed initial density field, with a smaller number of peaks than expected, but recovers the PDF of the initial density with impressive accuracy on scales as small as 3Mpc/h.Comment: 39 pages, including 13 Figures, submitted to Ap

Reconstruction Analysis of Galaxy Redshift Surveys: A Hybrid Reconstruction Method

In reconstruction analysis of galaxy redshift surveys, one works backwards from the observed galaxy distribution to the primordial density field in the same region, then evolves the primordial fluctuations forward in time with an N-body code. This incorporates assumptions about the cosmological parameters, the properties of primordial fluctuations, and the biasing relation between galaxies and mass. These can be tested by comparing the reconstruction to the observed galaxy distribution, and to peculiar velocity data. This paper presents a hybrid reconstruction method that combines the `Gaussianization'' technique of Weinberg(1992) with the dynamical schemes of Nusser & Dekel(1992) and Gramann(1993). We test the method on N-body simulations and on N-body mock catalogs that mimic the depth and geometry of the Point Source Catalog Redshift Survey and the Optical Redshift Survey. This method is more accurate than Gaussianization or dynamical reconstruction alone. Matching the observed morphology of clustering can limit the bias factor b, independent of Omega. Matching the cluster velocity dispersions and z-space distortions of the correlation function xi(s,mu) constrains the parameter beta=Omega^{0.6}/b. Relative to linear or quasi-linear approximations, a fully non-linear reconstruction makes more accurate predictions of xi(s,mu) for a given beta, thus reducing the systematic biases of beta measurements and offering further scope for breaking the degeneracy between Omega and b. It also circumvents the cosmic variance noise that limits conventional analyses of xi(s,mu). It can also improve the determination of Omega and b from joint analyses of redshift & peculiar velocity surveys as it predicts the fully non-linear peculiar velocity distribution at each point in z-space.Comment: 72 pages including 33 figures, submitted to Ap

Rejuvenating Power Spectra II: the Gaussianized galaxy density field

We find that, even in the presence of discreteness noise, a Gaussianizing transform (producing a more-Gaussian one-point distribution) reduces nonlinearities in the power spectra of cosmological matter and galaxy density fields, in many cases drastically. Although Gaussianization does increase the effective shot noise, it also increases the power spectrum's fidelity to the linear power spectrum on scales where the shot noise is negligible. Gaussianizing also increases the Fisher information in the power spectrum in all cases and resolutions, although the gains are smaller in redshift space than in real space. We also find that the gain in cumulative Fisher information from Gaussianizing peaks at a particular grid resolution that depends on the sampling level.Comment: Slight changes to match version accepted to ApJ. 7 pages, 8 figure

Intrinsic Alignment in redMaPPer clusters -- II. Radial alignment of satellites toward cluster centers

We study the orientations of satellite galaxies in redMaPPer clusters constructed from the Sloan Digital Sky Survey at $0.1<z<0.35$ to determine whether there is any preferential tendency for satellites to point radially toward cluster centers. We analyze the satellite alignment (SA) signal based on three shape measurement methods (re-Gaussianization, de Vaucouleurs, and isophotal shapes), which trace galaxy light profiles at different radii. The measured SA signal depends on these shape measurement methods. We detect the strongest SA signal in isophotal shapes, followed by de Vaucouleurs shapes. While no net SA signal is detected using re-Gaussianization shapes across the entire sample, the observed SA signal reaches a statistically significant level when limiting to a subsample of higher luminosity satellites. We further investigate the impact of noise, systematics, and real physical isophotal twisting effects in the comparison between the SA signal detected via different shape measurement methods. Unlike previous studies, which only consider the dependence of SA on a few parameters, here we explore a total of 17 galaxy and cluster properties, using a statistical model averaging technique to naturally account for parameter correlations and identify significant SA predictors. We find that the measured SA signal is strongest for satellites with the following characteristics: higher luminosity, smaller distance to the cluster center, rounder in shape, higher bulge fraction, and distributed preferentially along the major axis directions of their centrals. Finally, we provide physical explanations for the identified dependences, and discuss the connection to theories of SA.Comment: 25 pages, 16 figures, 7 tables, accepted to MNRAS. Main statistical analysis tool changed, with the results remain simila

Quantifying Tensions between CMB and Distance Datasets in Models with Free Curvature or Lensing Amplitude

Recent measurements of the Cosmic Microwave Background (CMB) by the Planck Collaboration have produced arguably the most powerful observational evidence in support of the standard model of cosmology, i.e. the spatially flat $\Lambda$CDM paradigm. In this work, we perform model selection tests to examine whether the base CMB temperature and large scale polarization anisotropy data from Planck 2015 (P15) prefer any of eight commonly used one-parameter model extensions with respect to flat $\Lambda$CDM. We find a clear preference for models with free curvature, $\Omega_\mathrm{K}$, or free amplitude of the CMB lensing potential, $A_\mathrm{L}$. We also further develop statistical tools to measure tension between datasets. We use a Gaussianization scheme to compute tensions directly from the posterior samples using an entropy-based method, the surprise, as well as a calibrated evidence ratio presented here for the first time. We then proceed to investigate the consistency between the base P15~CMB data and six other CMB and distance datasets. In flat $\Lambda$CDM we find a $4.8\sigma$ tension between the base P15~CMB data and a distance ladder measurement, whereas the former are consistent with the other datasets. In the curved $\Lambda$CDM model we find significant tensions in most of the cases, arising from the well-known low power of the low-$\ell$ multipoles of the CMB data. In the flat $\Lambda$CDM $+A_\mathrm{L}$ model, however, all datasets are consistent with the base P15~CMB observations except for the CMB lensing measurement, which remains in significant tension. This tension is driven by the increased power of the CMB lensing potential derived from the base P15~CMB constraints in both models, pointing at either potentially unresolved systematic effects or the need for new physics beyond the standard flat $\Lambda$CDM model.Comment: 16 pages, 8 figures, 6 table