Footprints of Statistical Anisotropies

Abstract

We propose and develop a formalism to describe and constrain statistically anisotropic primordial perturbations. Starting from a decomposition of the primordial power spectrum in spherical harmonics, we find how the temperature fluctuations observed in the CMB sky are directly related to the coefficients in this harmonic expansion. Although the angular power spectrum does not discriminate between statistically isotropic and anisotropic perturbations, it is possible to define analogous quadratic estimators that are direct measures of statistical anisotropy. As a simple illustration of our formalism we test for the existence of a preferred direction in the primordial perturbations using full-sky CMB maps. We do not find significant evidence supporting the existence of a dipole component in the primordial spectrum.

26 pages, 5 double figures. Uses RevTeX4

References in corpus (19)

• Gravity, Lorentz Violation, and the Standard Model
• The axis of evil
• Is the low-l microwave background cosmic?
• Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
• Cosmic homogeneity demonstrated with luminous red galaxies
• Evidence of vorticity and shear at large angular scales in the WMAP data: a violation of cosmological isotropy?
• On the large-angle anomalies of the microwave sky
• Could dark energy be vector-like?
• On Foreground Removal from the Wilkinson Microwave Anisotropy Probe Data by an Internal Linear Combination Method: Limitations and Implications
• Spontaneous Isotropy Breaking: A Mechanism for CMB Multipole Alignments
• Measuring Statistical isotropy of the CMB anisotropy
• Is the Universe odd?
• The Virgo Alignment Puzzle in Propagation of Radiation on Cosmological Scales
• Assessing the effects of foregrounds and sky removal in WMAP
• Statistical Isotropy of the Wilkinson Microwave Anisotropy Probe Data: A Bipolar Power Spectrum Analysis
• Cosmic microwave background anisotropies in multi-connected flat spaces
• Principal Power of the CMB
• Template fitting and the large-angle CMB anomalies
• The Cosmic Microwave Background Bipolar Power Spectrum: Basic Formalism and Applications

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• Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum
• CMB Anisotropies and Inflation from Non-Standard Spinors
• Anisotropic Dark Energy: Dynamics of Background and Perturbations
• Primordial statistical anisotropy generated at the end of inflation
• Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data
• Imprints of anisotropic inflation on the cosmic microwave background
• Testable polarization predictions for models of CMB isotropy anomalies
• Broken Isotropy from a Linear Modulation of the Primordial Perturbations
• Direction-Dependent CMB Power Spectrum and Statistical Anisotropy from Noncommutative Geometry
• Testing Isotropy of Cosmic Microwave Background Radiation
• Creating Statistically Anisotropic and Inhomogeneous Perturbations
• Signals of Statistical Anisotropy in WMAP Foreground-Cleaned Maps
• An Estimator for statistical anisotropy from the CMB bispectrum
• Bayesian Limits on Primordial Isotropy Breaking
• Erratum: Statistical anisotropy in the inflationary universe
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• Effective Field Theory of Anisotropic Inflation and Beyond
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