Anomalous spacings of the CMB temperature angular power spectrum
  We propose a novel technique to analyse spacings of the observed CMB
temperature angular power spectrum (APS) motivated by the behaviour of level
spacings in the presence or absence of correlations between eigenvalues of a
random matrix. We use data from WMAP 9 year ILC and 2018 Planck maps
(Commander, NILC and SMICA) and estimate minimum, maximum, average spacings and
ratios of maximum to minimum spacings between consecutive multipoles of APS
measures ($C_{\ell}$ and $\frac{\ell(\ell+1)}{2\pi}C_\ell$). Anomalous
multipole ranges given by $\ell_{max}$ and $\ell_{min}$ exist for multipoles
$\in[2,31]$ of this work. Sans parity distinctions, average spacing of
$8\leq\ell \leq 31$ for $C_\ell$'s, and maximum and average spacings of
$\ell_{min}\in[8,12]$ of $\frac{\ell(\ell+1)}{2\pi}C_\ell$'s are anomalously
low for all maps, with most anomalously low maximum spacing at $99.93\%$ C.L.
for $\frac{\ell(\ell+1)}{2\pi}C_\ell\text{ (Planck NILC)}$. With parity
distinctions, even multipoles indicate anomalously low maximum and average
spacings relative to odd multipoles, most consistently for
$\ell_{max}\in[6,30]$ of $C_\ell$'s of all maps, the most outstanding being the
even multipole average spacing of $2\leq\ell\leq27$ for
$\frac{\ell(\ell+1)}{2\pi}C_\ell\text{ (WMAP)}$, at $99.60\%$ C.L. For spacing
ratios, multipole ranges are similar to those for anomalous spacings, and odd
multipole spacing ratios are mostly anomalous, with odd multipole spacing ratio
of $2\leq\ell\leq7$ being consistently low for all maps. Overall, we infer an
unusual deficit of correlations between APS measures and deviations from
isotropy due to consistently low, parity-biased anomalous spacings, which can
be argued to have arisen primordially. The physical origin of these findings
may be probed in future work.
