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.
Author
Merkel, Philipp M.; Schäfer, Björn Malte
Journal
Monthly Notices of the Royal Astronomical Society,
Paper Publication Date
October 2015
Paper Type
Astrostatistics