In this article, we propose a novel technique to test for anomalous features in the CMB. We analyse separations of the observed CMB angular power spectrum (C ) using temperature anisotropy data from WMAP 9 year ILC and 2018 Planck maps of Commander, NILC and SMICA. We estimate the minimum, maximum, average separations and ratios of the maximum to minimum separations between consecutive multipoles of the weighted spectrum, f ( )C . We see that such f ( )'s with higher multipole powers mitigate the parity asymmetry anomaly. For anomalous separations, we find that data exhibits anomalous ranges of multipoles defined by different max and min values, specifically for the entire range of multipoles from 2 − 31 of this work. Without parity based distinctions, most significantly, the maximum separation of the range 8 ≤ ≤ 31 is seen to be anomalously low at the 99.93% confidence level for f ( ) = (WMAP), ( +1) 2π (Planck NILC), the latter indicating a strong deviation from the Sachs-Wolfe plateau for maximum separations among low multipoles. The analysis is repeated for odd and even multipoles taken separately, in the same multipole ranges. Most noticeably, the even multipoles are seen to have anomalously low maximum and average separations relative to their odd counterparts, the most outstanding among which is the anomalously low maximum separation for even multipoles in the range 6 ≤ ≤ 31 for f ( ) = (WMAP), at the 99.77% confidence level. For separation ratios, the multipole ranges are similar to those which turn up as anomalous when only separations are considered.
Breakdown of rotational invariance of the primordial power spectrum manifests in the statistical anisotropy of the observed Cosmic Microwave Background (CMB) radiation. Hemispherical power asymmetry in the CMB may be caused due to a dipolar modulation, indicating the presence of a preferred direction. Appropriately rescaled local variance maps of the CMB temperature anisotropy data effectively encapsulate this dipolar pattern. As a first-of-its-kind method, we train Artificial Neural Networks (ANNs) with such local variances as input features to distinguish statistically isotropic CMB maps from dipole-modulated ones. Our trained ANNs are able to predict components of the amplitude times the unit vector of the preferred direction for mixed sets of modulated and unmodulated maps, with goodness-of-fit (R
2) scores >0.97 for full sky and >0.96 for partial sky coverage. On all observed foreground-cleaned CMB maps, the ANNs detect the dipolar modulation signal with overall consistent values of amplitudes and directions. This detection is significant at 97.21%–99.38% C.L. for all full sky maps, and at 98.34%–100% C.L. for all partial sky maps. Robustness of the signal holds across full and partial skies, various foreground cleaning methods, inpainting algorithms, instruments, and all the different periods of observation for Planck and WMAP satellites. The significant and robust detection of the signal, in addition to the consistency of values of amplitude and directions, as found independent of any preexisting methods, further mitigates the criticisms of look-elsewhere effects and a posteriori inferences for the preferred dipole direction in the CMB.
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