skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Shape of high order correlation functions in CMB anisotropy maps

Abstract

We present a phenomenological investigation of non-Gaussian effects that could be seen on CMB temperature maps. Explicit expressions for the temperature correlation functions are given for different types of primordial mode couplings. We argue that a simplified description of the radial transfer function for the temperature anisotropies allows one to get insights into the general properties of the bispectrum and trispectrum. The accuracy of these results is explored together with the use of the small scale approximation to get explicit expressions of high order spectra. The bispectrum is found to have alternate signs for the successive acoustic peaks. Sign patterns for the trispectrum are more complicated and depend specifically on the type of metric couplings. Local primordial couplings are found to give patterns that are different from those expected from weak lensing effects.

Authors:
;  [1]
  1. Service de Physique Theorique, CEA/DSM/SPhT, Unite de Recherche Associee au CNRS, CEA/Saclay 91191 Gif-sur-Yvette Cedex (France)
Publication Date:
OSTI Identifier:
20782895
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.73.083524; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; APPROXIMATIONS; CORRELATION FUNCTIONS; COSMIC RADIATION; COSMOLOGY; ENERGY SPECTRA; RADIOWAVE RADIATION; TRANSFER FUNCTIONS

Citation Formats

Brunier, Tristan, and Bernardeau, Francis. Shape of high order correlation functions in CMB anisotropy maps. United States: N. p., 2006. Web. doi:10.1103/PHYSREVD.73.083524.
Brunier, Tristan, & Bernardeau, Francis. Shape of high order correlation functions in CMB anisotropy maps. United States. doi:10.1103/PHYSREVD.73.083524.
Brunier, Tristan, and Bernardeau, Francis. Sat . "Shape of high order correlation functions in CMB anisotropy maps". United States. doi:10.1103/PHYSREVD.73.083524.
@article{osti_20782895,
title = {Shape of high order correlation functions in CMB anisotropy maps},
author = {Brunier, Tristan and Bernardeau, Francis},
abstractNote = {We present a phenomenological investigation of non-Gaussian effects that could be seen on CMB temperature maps. Explicit expressions for the temperature correlation functions are given for different types of primordial mode couplings. We argue that a simplified description of the radial transfer function for the temperature anisotropies allows one to get insights into the general properties of the bispectrum and trispectrum. The accuracy of these results is explored together with the use of the small scale approximation to get explicit expressions of high order spectra. The bispectrum is found to have alternate signs for the successive acoustic peaks. Sign patterns for the trispectrum are more complicated and depend specifically on the type of metric couplings. Local primordial couplings are found to give patterns that are different from those expected from weak lensing effects.},
doi = {10.1103/PHYSREVD.73.083524},
journal = {Physical Review. D, Particles Fields},
number = 8,
volume = 73,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}
  • We propose an alternative formalism to simulate cosmic microwave background (CMB) temperature maps in {lambda}CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial sections. Instead, the covariance matrix of the coefficients of the spherical harmonic decomposition of the temperature anisotropies is expressed in terms of the elements of the covering group of the space. We obtain a decomposition of the correlation matrix that isolates the topological contribution to the CMB temperature anisotropies out of the simply connected contribution. A further decomposition of the topological signature ofmore » the correlation matrix for an arbitrary topology allows us to compute it in terms of correlation matrices corresponding to simpler topologies, for which closed quadrature formulas might be derived. We also use this decomposition to show that CMB temperature maps of (not too large) multiply connected universes must show ''patterns of alignment,'' and propose a method to look for these patterns, thus opening the door to the development of new methods for detecting the topology of our Universe even when the injectivity radius of space is slightly larger than the radius of the last scattering surface. We illustrate all these features with the simplest examples, those of flat homogeneous manifolds, i.e., tori, with special attention given to the cylinder, i.e., T{sup 1} topology.« less
  • Bianchi VII{sub h} models have been recently proposed to explain potential anomalies in the CMB anisotropy as observed by WMAP. We investigate the violation of statistical isotropy due to an embedded Bianchi VII{sub h} template in the CMB anisotropy maps to determine whether the existence of a hidden Bianchi template in the WMAP data is consistent with the previous null detection of the bipolar power spectrum in the WMAP first-year maps. We argue that, although correcting the WMAP maps for the Bianchi template may explain some features in the WMAP data, it may cause other anomalies such as preferred directionsmore » leading to detectable levels of violation of statistical isotropy in the Bianchi corrected maps. We compute the bipolar power spectrum for the low density Bianchi VII{sub h} models embedded in the background CMB anisotropy maps with the power spectrum that have been shown in recent literature to best fit the first-year WMAP data. By examining the statistical isotropy of these maps, we put a limit of (({sigma}/H)){sub 0}{<=}2.77x10{sup -10}(99% C.L.) on the shear parameter in Bianchi VII{sub h} models.« less
  • In recent years the goal of estimating different cosmological parameters precisely has set new challenges in the effort to accurately measure the angular power spectrum of the CMB. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel, model-independent method for the estimation of the CMB angular power spectrum solely from multifrequency observations has been proposed and implemented on the first year WMAP data by Saha et al. 2006. All previous estimates of the power spectrum of the CMB are based upon foreground templates using data sets from different experiments.more » However, our methodology demonstrates that the CMB angular spectrum can be reliably estimated with precision from a self-contained analysis of the WMAP data. In this work we provide a detailed description of this method. We also study and identify the biases present in our power spectrum estimate. We apply our methodology to extract the power spectrum from the WMAP data.« less
  • We use wavelet and curvelet transforms to extract signals of cosmic strings from simulated cosmic microwave background (CMB) temperature anisotropy maps, and to study the limits on the cosmic string tension which various ongoing CMB temperature anisotropy experiments will be able to achieve. We construct sky maps with size and angular resolution corresponding to various experiments. These maps contain the signals of a scaling solution of long string segments with a given string tension G μ, the contribution of the dominant Gaussian primordial cosmological fluctuations, and pixel by pixel white noise with an amplitude corresponding to the instrumental noise ofmore » the various experiments. In the case that we include white noise, we find that using curvelets we obtain lower bounds on the string tension than with wavelets. For maps with Planck specification, we obtain bounds comparable to what was obtained by the Planck collaboration [1]. Experiments with better angular resolution such as the South Pole Telescope third generation (SPT-3G) survey will be able to yield stronger limits. For maps with a specification of SPT-3G we find that string signals will be visible down to a string tension of G μ = 1.4 × 10{sup −7}.« less
  • y-type spectral distortions of the cosmic microwave background allow us to detect clusters and groups of galaxies, filaments of hot gas and the non-uniformities in the warm hot intergalactic medium. Several CMB experiments (on small areas of sky) and theoretical groups (for full sky) have recently published y-type distortion maps. We propose to search for two artificial hot spots in such y-type maps resulting from the incomplete subtraction of the effect of the motion induced dipole on the cosmic microwave background sky. This dipole introduces, at second order, additional temperature and y-distortion anisotropy on the sky of amplitude few μKmore » which could potentially be measured by Planck HFI and Pixie experiments and can be used as a source of cross channel calibration by CMB experiments. This y-type distortion is present in every pixel and is not the result of averaging the whole sky. This distortion, calculated exactly from the known linear dipole, can be subtracted from the final y-type maps, if desired.« less