Anomalous separations of the CMB temperature angular power spectrum

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 ($C_\ell$) 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, $f(\ell)C_{\ell}$. We see that such $f(\ell)$'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 $\ell_{max}$ and $\ell_{min}$ 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 $8\leq\ell\leq31$ is seen to be anomalously low at the $99.93\%$ confidence level for $f(\ell)=\ell$ (WMAP), $\frac{\ell(\ell+1)}{2\pi}$ (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 $6\leq\ell\leq31$ for $f(\ell)=\ell$ (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.