Investigating non-Gaussianity in Cosmic Microwave Background temperature maps using spherical harmonic phases

In the era of precision cosmology, accurate estimation of cosmological parameters is based upon the implicit assumption of the Gaussian nature of Cosmic Microwave Background (CMB) radiation. Therefore, an important scientific question to ask is whether the observed CMB map is consistent with Gaussian prediction. In this work, we extend previous studies based on CMB spherical harmonic phases (SHP) to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field (GRF). The null hypothesis is that the corresponding CMB SHP are independent and identically distributed in terms of a uniform distribution in the interval [0, 2π] [1,2]. We devise a new model-independent method where we use ordered and non-parametric Rao's statistic, based on sample arc-lengths to comprehensively test uniformity and independence of SHP for a given ℓ mode and independence of nearby ℓ mode SHP. We performed our analysis on the scales limited by spherical harmonic modes ≤ 128, to restrict ourselves to signal-dominated regions. To find the non-uniform or dependent sets of SHP, we calculate the statistic for the data and 10000 Monte Carlo simulated uniformly random sets of SHP and use 0.05 and 0.001 α levels to distinguish between statistically significant and highly significant detections. We first establish the performance of our method using simulated Gaussian, non-Gaussian CMB temperature maps, along with observed non-Gaussian 100 and 143 GHz Planck channel maps. We find that our method, performs efficiently and accurately in detecting phase correlations generated in all of the non-Gaussian simulations and observed foreground contaminated 100 and 143 GHz Planck channel temperature maps. We apply our method on Planck satellite mission's final released CMB temperature anisotropy maps- COMMANDER, SMICA, NILC, and SEVEM along with WMAP 9 year released ILC map. We report that SHP corresponding to some of the m-modes are non-uniform, some of the ℓ mode SHP and neighboring mode pair SHP are correlated in cleaned CMB maps. The detection of non-uniformity or correlation in the SHP indicates the presence of non-Gaussian signals in the foreground minimized CMB maps.

The Statistical Analysis of Anisotropy Fluctuations of CMB Temperature in Angular Spatial and Temporal Areas

The changes in the nature of the statistical distributions of the anisotropy of the temperature of CMB in the satellite measurements of the “WMAP” probe were analyzed for the presence of laws in them in changes within the adjacent periods of data accumulation. Statistical distributions of changes in anisotropy between adjacent data accumulation periods were analyzed. The probability of the occurrence of such unidirectional changes at different frequencies of satellite measurements was analyzed and the probability of their occurrence under the influence of non-random factors was estimated.

Evolution of virial clouds-I: from surface of last scattering up to the formation of population-III stars

The analysis of WMAP and Planck CMB data has shown the presence of temperature asymmetries towards the halos of several galaxies, which is probably due to the rotation of clouds present in these halos about the rotational axis of the galaxies. It had been proposed that these are hydrogen clouds that should be in equilibrium with the CMB. However, standard theory did not allow equilibrium of such clouds at the very low CMB temperature, but it was recently shown that the equilibrium could be stable. This still does not prove that the cloud concentration and that the observed temperature asymmetry is due to clouds in equilibrium with the CMB. To investigate the matter further, it would be necessary to trace the evolution of such clouds, which we call “virial clouds”, from their formation epoch to the present, so as to confront the model with the observational data. The task is to be done in two steps: (1) from the cloud formation before the formation of first generation of stars; (2) from that time to the present. In this paper we deal with the first step leaving the second one to a subsequent analysis.

A new probe of Gaussianity and isotropy with application to cosmic microwave background maps

We introduce a new mathematical tool (a direction-dependent probe) to analyze the randomness of purported isotropic Gaussian random fields on the sphere. If the field is isotropic and Gaussian then the probe coefficients for a given direction should be realizations of uncorrelated scalar Gaussian random variables. To study the randomness of a field, we use the autocorrelation of the sequence of probe coefficients (which are just the Fourier coefficients [Formula: see text] if the [Formula: see text]-axis is taken in the probe direction). We introduce a particular function on the sphere (called the AC discrepancy) that accentuates the departure from Gaussianity and isotropy. We apply the probe to assess the full-sky cosmic microwave background (CMB) temperature maps produced by the Planck collaboration (PR2 2015 and PR3 2018), with special attention to the inpainted maps. We find that for some of the maps, there are many directions for which the departures are significant, especially near the galactic plane. We also look briefly at the noninpainted Planck maps, for which the computed AC discrepancy maps have a very different character, with features that are global rather than local.