Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum

TL;DR

This paper develops statistical tools to detect and analyze direction-dependent anisotropies in the primordial power spectrum using cosmic microwave background data, enabling tests of isotropy assumptions in cosmology.

Contribution

It introduces new estimators for anisotropy in the primordial power spectrum and demonstrates their application to detect quadrupole anisotropy with Planck data.

Findings

Detectable quadrupole anisotropy as small as 2.0% with Planck.

Development of model-independent and spherical-harmonic estimators for anisotropy.

Application to an inflation model with directional dependence.

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 wavevector. 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 direction-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.