Analysis of non-Gaussian CMB maps based on the N-pdf. Application to WMAP data

Abstract

We present a new method based on the N-point probability distribution (pdf) to study non-Gaussianity in cosmic microwave background (CMB) maps. Likelihood and Bayesian estimation are applied to a local non-linear perturbed model up to third order, characterized by a linear term which is described by a Gaussian N-pdf, and a second and third order terms which are proportional to the square and the cube of the linear one. We also explore a set of model selection techniques (the Akaike and the Bayesian Information Criteria, the minimum description length, the Bayesian Evidence and the Generalized Likelihood Ratio Test) and their application to decide whether a given data set is better described by the proposed local non-Gaussian model, rather than by the standard Gaussian temperature distribution. As an application, we consider the analysis of the WMAP 5-year data at a resolution of around 2 degrees. At this angular scale (the Sachs-Wolfe regime), the non-Gaussian description proposed in this work defaults (under certain conditions) to an approximative local form of the weak non-linear coupling inflationary model (e.g. Komatsu & Spergel 2001) previously addressed in the literature. For this particular case, we obtain an estimation for the non-linear coupling parameter of -94 < F_nl < 154 at 95% CL. Equally, model selection criteria also indicate that the Gaussian hypothesis is favored against the particular local non-Gaussian model proposed in this work. This result is in agreement with previous findings obtained for equivalent non-Gaussian models and with different non-Gaussian estimators. However, our estimator based on the N-pdf is more efficient than previous estimators and, therefore, provides tighter constraints on the coupling parameter at degree angular resolution.

13 pages, 4 figures. Minor changes. Accepted for publication in MNRAS

References in corpus (42)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Information criteria for astrophysical model selection
• Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes
• Imprints of a Primordial Preferred Direction on the Microwave Background
• Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps
• Detection of primordial non-Gaussianity (fNL) in the WMAP 3-year data at above 99.5% confidence
• Instability of anisotropic cosmological solutions supported by vector fields
• The non-Gaussian Cold Spot in the 3-year WMAP data
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Foreground Emission
• Angular Trispectrum of CMB Temperature Anisotropy from Primordial Non-Gaussianity with the Full Radiation Transfer Function
• CMB Anisotropies and Inflation from Non-Standard Spinors
• A Cosmic Microwave Background feature consistent with a cosmic texture
• Instability of the ACW model, and problems with massive vectors during inflation
• Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data
• The Axis of Evil revisited
• Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies
• Top ten accelerating cosmological models
• Present and future evidence for evolving dark energy
• Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results
• A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I
• The CMB cold spot: texture, cluster or void?
• Bianchi Type VII_h Models and the WMAP 3-year Data
• Global universe anisotropy probed by the alignment of structures in the cosmic microwave background
• Broken Isotropy from a Linear Modulation of the Primordial Perturbations
• On the CMB large-scales angular correlations
• Alignment tests for low CMB multipoles
• Accelerated Cosmological Models in Modified Gravity tested by distant Supernovae SNIa data
• A low CMB variance in the WMAP data
• Markov chain Monte Carlo analysis of Bianchi VII_h models
• Alignment and signed-intensity anomalies in WMAP data
• WMAP 3-year primordial power spectrum
• WMAP 5-year constraints on fnl with wavelets
• A Scaling Index Analysis of the WMAP three year data: Signatures of non-Gaussianities and Asymmetries in the CMB
• Genus Topology of the Cosmic Microwave Background from the WMAP 3-Year Data
• Non-Gaussianity analysis on local morphological measures of WMAP data
• Steerable wavelet analysis of CMB structures alignment
• Bianchi VII_h models and the cold spot texture
• Testing and selection of cosmological models with $(1+z{)}^6$ corrections
• Planck and reionization history: a model selection view
• Testing Gaussianity on Archeops Data

Cited by in corpus (24)

• Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background
• Primordial Non-Gaussianity in the Cosmic Microwave Background
• Constraints on f_nl and g_nl from the analysis of the N-pdf of the CMB large scale anisotropies
• Improved constraints on primordial non-Gaussianity for the Wilkinson Microwave Anisotropy Probe 5-yr data
• Baryon history and cosmic star formation in non-Gaussian cosmological models: numerical simulations
• Local analyses of Planck maps with Minkowski Functionals
• Non-gaussianity in the foreground-reduced CMB maps
• Is the cold spot responsible for the CMB North-South asymmetry?
• North-South non-Gaussian asymmetry in PLANCK CMB maps
• Local non-Gaussianity in the Cosmic Microwave Background the Bayesian way
• Constraints on general primordial non-Gaussianity using wavelets for the Wilkinson Microwave anisotropy probe 7-year data
• Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator
• On the optimality of the spherical Mexican hat wavelet estimator for the primordial non-Gaussianity
• Wilkinson Microwave Anisotropy Probe 7-yr constraints on fNL with a fast wavelet estimator
• A weak lensing view on primordial non-Gaussianities
• Statistics of the excursion sets in models with local primordial non-Gaussianity
• A test of the Suyama-Yamaguchi inequality from weak lensing
• Joint constraints on galaxy bias and ${\sigma }_8$ through the N-pdf of the galaxy number density
• On the regularity of the covariance matrix of a discretized scalar field on the sphere
• An overview of the current status of CMB observations
• Non-Gaussianity in the HILC foreground-reduced three-year WMAP CMB map
• A Study of Gaussianity in CMB band maps
• Investigating non-Gaussianity in Cosmic Microwave Background Temperature Maps using Spherical Harmonic Phases
• Non-Gaussian Distribution and Clustering of Hot and Cold Pixels in the WMAP Five-Year Sky