Isotropy statistics of CMB hot and cold spots

Abstract Statistical Isotropy of the Cosmic Microwave Background (CMB) radiation has been studied and debated extensively in recent years. Under this assumption, hot spots cold CMB are expected to be uniformly distributed over a 2-sphere. We use orientation matrix, first proposed by Watson (1965) Scheidegger associated shape strength parameters (Woodcock, 1977) analyse whether observed temperature anisotropy field placed. demonstrate usefulness our estimators using simulated toy models containing non-uniform data. apply method on several foreground minimized maps WMAP Planck large angular scales. The constrain geometric features possible deviations from uniformity (isotropy) power anomalous signal. find that distributions or cleaned show no unusual signature clustering girdling. Instead, we notice strikingly uniform distribution full sky. signal remains robust with respect four used presence absence non-Gaussian spot (NGCS). On partial sky KQ75 U73 masks anomalously low non-uniformity for which is found various cleaning methods, applied, instruments, frequencies, NGCS. Interestingly weak could due contributions quadrupole octupole may related variance anomaly.