Extreme value statistics of CMB lensing deflection angles

TL;DR

This study analyzes the extreme values of CMB lensing deflection angles using extreme value statistics, considering the effects of filtering and reconstruction noise, and finds limited potential for constraining cosmological models.

Contribution

It applies extreme value statistics to CMB lensing deflection fields, accounting for filtering and noise, and assesses their effectiveness in cosmological constraints.

Findings

Maxima and minima follow Weibull-type distributions

Filtering and noise significantly affect the statistics

Limited potential for cosmological model constraints

Abstract

The smaller the angular scales on which the anisotropies of the cosmic microwave background (CMB) are probed the more important their distortion due to gravitational lensing becomes. Here we investigate the maxima and minima of the CMB lensing deflection field using general extreme value statistics. Since general extreme value statistics applies to uncorrelated data in first place we consider appropriately low-pass filtered deflection maps. Besides the suppression of correlations filtering is required for another reason: The lensing field itself is not directly observable but needs to be (statistically) reconstructed from the lensed CMB by means of a quadratic estimator. This reconstruction, though, is noise dominated and therefore requires smoothing, too. In idealized Gaussian realizations as well as in realistically reconstructed data we find that both maxima and minima of the deflection angle components follow consistently a general extreme value distribution of Weibull-type. However, its shape, location and scale parameters vary significantly between different realizations. The statistics' potential power to constrain cosmological models appears therefore rather limited.