Cosmic microwave background statistics for a direction-dependent primordial power spectrum

2007/09/30 by Anthony R. Pullen, Marc Kamionkowski · 6 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Anisotropy #Astrophysics #Bispectrum #Cosmic microwave background #Cosmic variance #Cosmology #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Estimator #Geophysics and Gravity Measurements #Inflation (cosmology) #Isotropy #Mathematics #Physics #Planck #Polarization (electrochemistry) #Primordial fluctuations #Quadrupole #Quantum mechanics #Spectral density #Spherical harmonics #Statistical physics #Statistics #Theoretical physics #astro-ph

paper · pdf · doi:10.1103/physrevd.76.103529

published as Phys.Rev.D76:103529,2007 · Published in Phys. Rev. D; 8 pages; 1 table; Table 1 corrected; references added

openalex publication_date 2007/11/21 · arxiv created 2008/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Statistical isotropy of primordial perturbations is a common assumption in cosmology, but it is an assumption that should be tested. To this end, we develop cosmic microwave background statistics for a primordial power spectrum that depends on the direction, as well as the magnitude, of the Fourier wave vector. We first consider a simple estimator that searches in a model-independent way for anisotropy in the square of the temperature (and/or polarization) fluctuation. We then construct the minimum-variance estimators for the coefficients of a spherical-harmonic expansion of the directional dependence of the primordial power spectrum. To illustrate, we apply these statistics to an inflation model with a quadrupole dependence of the primordial power spectrum on direction and find that a power quadrupole as small as 2.0% can be detected with the Planck satellite.

Citations

• Examination of Evidence for a Preferred Axis in the Cosmic Radiation Anisotropy
• Anisotropic perturbations due to dark energy
• Measuring the Small-Scale Power Spectrum of Cosmic Density Fluctuations through 21 cm Tomography Prior to the Epoch of Structure Formation
• Asymmetric inflation: Exact solutions
• Template fitting and the large-angle cosmic microwave background anomalies
• Steerable wavelet analysis of CMB structures alignment
• TheN‐Point Correlation Functions of the First‐YearWilkinson Microwave Anisotropy ProbeSky Maps
• Is the Low-ℓMicrowave Background Cosmic?
• Signature of Gravity Waves in the Polarization of the Microwave Background
• The Axis of Evil revisited
• On the large-angle anomalies of the microwave sky
• Occam's razor meets WMAP
• Statistics of cosmic microwave background polarization

Cited by

• Cosmological magnetic fields from inflation and backreaction
• Vector field models of inflation and dark energy
• Primordial non-Gaussianities in single field inflationary models with non-trivial initial states
• Future CMB constraints on cosmic birefringence and implications for fundamental physics
• Chirality of the gravitational-wave background and pulsar-timing arrays
• Spectator electric fields, de Sitter spacetime, and the Schwinger effect