Angular-planar CMB power spectrum

TL;DR

This paper introduces a new statistical test to detect deviations from isotropy in the CMB by analyzing angular and planar modulations of the temperature power spectrum, revealing slight anomalies in WMAP data.

Contribution

The paper presents a novel angular-planar power spectrum estimator and a statistical test for detecting anisotropies in the CMB, extending traditional methods.

Findings

Detected slight anomalies at $l=7$ and $l=8$ in WMAP data

Developed an unbiased estimator for the angular-planar power spectrum

Provided a model-independent method for anisotropy detection

Abstract

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum $C_l$, this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual $C_l$'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales $l=7$ and $l=8$. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.