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In this article, we extend previous studies based on CMB spherical harmonicphases (SHP) to examine the validity of the hypothesis that the temperaturefield of the CMB is consistent with a Gaussian random field (GRF). The nullhypothesis is that the corresponding CMB SHP are independent and identicallydistributed in terms of a uniform distribution in the interval [0, 2$\pi$]\citep{1986ApJ...304...15B,2013rossmanith}. We devise a new model-independentmethod where we use ordered and non-parametric Rao's statistic, based on samplearc-lengths to comprehensively test uniformity and independence of SHP. Weperformed our analysis on the scales limited by spherical harmonic modes $\le$128, to restrict ourselves to signal-dominated regions. To find the non-uniformor dependent sets of SHP, we calculate the statistic for the data and 10000Monte Carlo simulated uniformly random sets of SHP and use 0.05 and 0.001$\alpha$ levels to distinguish between statistically significant and highlysignificant detections. We first establish the performance of our method usingsimulated Gaussian, non-Gaussian CMB temperature maps, along with observednon-Gaussian 100 and 143 GHz Planck channel maps. We find that our methodperforms efficiently and accurately in detecting phase correlations generatedin all of the non-Gaussian simulations and observed foreground contaminated 100and 143 GHz Planck channel temperature maps. We apply our method on the Plancksatellite mission's final released CMB temperature anisotropy maps- COMMANDER,SMICA, NILC, and SEVEM along with WMAP 9 year released ILC map. We report thatSHP corresponding to some of the $m$-modes is non-uniform, some of the $\ell$mode SHP and neighboring mode pair SHP are correlated in cleaned CMB maps. Thedetection of non-uniformity or correlation in the SHP indicates the presence ofnon-Gaussian signals in the foreground minimized CMB maps.

Investigating non-Gaussianity in Cosmic Microwave Background Temperature Maps using Spherical Harmonic Phases