Clustering of local extrema in <i>Planck</i> CMB maps

ABSTRACT The clustering of local extrema will be exploited to examine Gaussianity, asymmetry, and the footprint cosmic-string network on CMB observed by Planck. number density (npk for peak ntr trough) sharp clipping (npix) statistics support Gaussianity hypothesis all component separations. However, pixel at threshold reveals a more consistent treatment with respect end-to-end simulations. A very tiny deviation from associated simulations in context trough density, range ? ? [?2–0] NILC CR separations, are detected. unweighted two-point correlation function, ?, illustrates good consistency between different separations corresponding Gaussian almost available thresholds. high thresholds, small deficit peaks is Planck fiducial ?CDM model. To put significant constraint amplitude mass function based value ? around Doppler (? ? 70–75 arcmin), we should consider ? 0.0. scale-independent bias factors above large separation angle level agreement expected pure CMB. Applying npk, ntr, ?pk ? pk ?tr tr measures tessellated map patches 7.52 deg2 size prove statistical isotropy maps. analysis puts upper bound tension, G?(up) 5.59 × 10?7, SMICA.