Level correlations of CMB temperature angular power spectrum

If the principle of statistical isotropy is valid, then angular power spectrum (APS) cosmic microwave background (CMB) radiation uncorrelated between different multipoles. We propose a novel technique to analyse any possible correlations foreground-cleaned CMB temperature APS measures ( $$C_{\ell }$$ and $${\mathcal {D}}_\ell =({\ell (\ell +1)})/({2\pi })C_\ell $$ ). This motivated by behaviour level spacings random matrix eigenvalues. method helps distinguish statistically isotropic from correlated APS, where latter can arise due breakdown or presence some residual systematics in foreground cleaned maps. Spacings $$C_\ell ’s are seen closely obey Poisson statistics introduction correlations, changes distribution appropriate Wigner–Dyson statistics. For CMB, we employ average spacing consecutive multipole for multipoles $$\in [2,31]$$ . estimator sensitive departures null hypothesis zero CMB. study full sky WMAP 9-year ILC 2018 Planck maps (Commander, NILC SMICA). Sans parity distinctions, good agreement with theoretical expectation. With even indicate unusually low both (at $$\ge 98.86% C.L.) $${\ge 95.07% C.L.). use an inpainting based on constrained Gaussian realisations show that U73 KQ75 masks, all inpainted robustly confirm existence such APS. In addition, this signal independent non-Gaussian cold spot.