Cosmic Microwave Background Maps Research Articles

Planck PR4 (NPIPE) map-space cosmic birefringence

Cosmic birefringence is an effect where the plane of polarisation of the cosmic microwave background (CMB) is rotated by an angle β through coupling to a hypothetical parity-violating field. We analyse the Planck Public Release 4 (PR4 or NPIPE) data using a map-space analysis method and find β= 0.46° ± 0.04°(stat.) ± 0.28°(syst.) for SEVEM CMB maps and β = 0.48° ± 0.04°(stat.) ± 0.28°(syst.) for Commander CMB maps.These values are slightly higher than previously published results, which may be explained by the fact that we have not attempted to remove any potential bias from miscalibration of the Planck polarimeters.The uncertainty in this miscalibration dominates the systematic uncertainty, which also means that our results are consistent with no parity violation. An advantage of the map-space analysis is that it is easy to investigate any variations on the sky, for example caused by foreground contamination. Our results for isotropic birefringence are fairly robust against different spatial data cuts, but there may be hints of a foreground systematic (north versus south hemispheres) or uncontrolled miscalibration effect (T peaks versus E peaks) that should be followed up in future studies. We additionally find noevidence of a cosmic birefringence dipole (anisotropic birefringence).

A p < 0.0001 detection of cosmic microwave background cooling in galactic halos and its possible relation to dark matter

We confirm, at the 5.7σ level, previous studies reporting cosmic microwave background (CMB) temperatures being significantly lower around nearby spiral galaxies than expected from the ΛCDM model. Results from our earlier work were disputed in a recent paper, however, that analysis included areas far beyond the galactic halos, while disregarding the neighbourhood of the galaxies where the main signal is seen. Here, we limit the present study to pixels that are well within the galactic halos, focussing on galaxies in dense cosmic filaments and improving the signal-to-noise ratio (S/N), as compared to previous studies. The average CMB temperature in discs around these galaxies is always much lower in Planck data than in any of the 10 000 Planck-like CMB simulations. Even when correcting for the look-elsewhere effect, the detection is still at the 3 − 4σ level. We further show that the largest scales (ℓ < 16) of the Planck CMB fluctuations are more correlated with the distribution of nearby galaxies than 99.99% of simulated CMB maps. We argue that the existence of a new CMB foreground cannot be ignored and a physical interaction mechanism should be sought, which could possibly involve dark matter and could also be linked to intergalactic magnetic fields.

The Direct Measurement of Gravitational Potential Decay Rate at Cosmological Scales. II. Improved Dark Energy Constraint from z ≤ 1.4

Abstract The gravitational potential decay rate (DR) is caused by the cosmic acceleration of the Universe, providing a direct probe into the existence of dark energy (DE). We present measurements of DR and explore its implications for DE models using the DR9 galaxy catalog of the Dark Energy Spectroscopic Instrument (DESI) imaging surveys and the Planck cosmic microwave background maps. Our analysis includes six redshift bins within the range of 0.2 ≤ z < 1.4 and achieves a total significance of 3.1σ, extending the DR measurements to a much higher redshift compared to Dong et al., which focused on 0.2 ≤ z < 0.8. Other improvements involve addressing potential systematics in the DR-related measurements of correlation functions, including imaging systematics and magnification bias. We explore the constraining power of DR on both the wCDM model and the w 0 w a CDM model. We find that the addition of DR can significantly improve the DE constraints, over Sloan Digital Sky Survey baryon acoustic oscillation (BAO) data alone or the PantheonPlus supernovae (SNe) compilation alone, although it shows only a modest improvement for DESI BAO. In the wCDM model, all three probes—DR, DESI BAO, and SNe—favor w = −1. For the w 0 w a CDM, while DESI BAO prefers w 0 > −1 and w a < 0, the SNe Ia and DR data constrain w 0 = − 0.9 4 − 0.13 + 0.11 and w a = − 0.2 2 − 0.97 + 0.57 . Namely, SNe Ia and DR data have no preference on dynamical DE over Λ.

Methods for CMB Map Analysis

Abstract There are standard tools for analyzing cosmic microwave background maps. However, several important details are not usually highlighted. Here we describe best practices for several common map-modifying procedures, including masking, downgrading resolution, convolving with beam and pixel window functions, and adding white noise. We will explore how these modifications affect the final power spectrum measured from a map. We recommend the best ways to perform each of these procedures, describe when the different steps and measures should be carried out, and show the effects of incorrectly performing or applying any of them.

ABCMB: deep delensing assisted likelihood-free inference from CMB polarization maps

Abstract The existence of a cosmic background of primordial gravitational waves is a robust prediction of inflationary cosmology, but it has so far evaded discovery. The most promising avenue of its detection is via measurements of cosmic microwave background (CMB) B-polarization. However, this is not straightforward due to (a) the fact that CMB maps are distorted by gravitational lensing and (b) the high-dimensional nature of CMB data, which renders likelihood-based analysis methods computationally extremely expensive. In this paper, we introduce an efficient likelihood-free, end-to-end inference method to directly infer the posterior distribution of the tensor-to-scalar ratio r from lensed maps of the Stokes Q and U polarization parameters. Our method employs a generative model to delense the maps and utilizes the approximate Bayesian computation algorithm to sample r. We demonstrate that our method yields unbiased estimates of r with well-calibrated uncertainty quantification.

On the (Higher Multipoles) Variance Asymmetry in the Cosmic Microwave Background

We have studied the cosmic microwave background (CMB) map looking for features beyond cosmological isotropy. We began by tiling the CMB variance maps (which are produced by different smoothing scales) with stripes of different sizes along the most prominent dipole direction. We were able to confirm previous findings regarding the significance of the dipole. Furthermore, we discovered that some of the higher multipoles exhibit significance comparable to the dipole that naturally depends on the smoothing scales. In the end, we discussed this result having an eye on the look-elsewhere-effect. We believe our results may indicate an anomalous patch in the CMB sky that warrants further investigation.

Does the Correlation between 2MRS Galaxies and the CMB Indicate an Unmodeled CMB Foreground?

We revisit the claimed detection of a new cosmic microwave background (CMB) foreground based on the correlation between low-redshift Two Micron All Sky Survey Redshift Survey (2MRS) galaxies and CMB temperature maps from the Planck and Wilkinson Microwave Anisotropy Probe missions. We reproduce the reported measurements but argue that the original analysis significantly underestimated the uncertainties. We cross-correlate the 2MRS galaxy positions with simulated CMB maps and show that the correlation measured with the real data for late-type spiral galaxies at angular scales θ ≥ 0.°1 and redshift cz < 4500 km s−1 is consistent with zero at the 1.7σ level or less, depending on the exact CMB map and simulation construction. This was the sample that formed the basis for the original detection claim. For smaller angular separations the results are not robust to galaxy type or CMB cleaning method, and we are unable to draw firm conclusions. The original analysis did not propose a specific, falsifiable physical correlation mechanism, and it is impossible to rule out any contribution from an underlying physical effect. However, given our calculations, the lack of signal from expanding the redshift range, and the lack of corroboration from other galaxy surveys, we do not find the evidence for a new CMB foreground signal compelling.

The anomaly of the CMB power with the latest Planck data

The lack of power anomaly is an unexpected feature observed at large angular scales in the maps of Cosmic Microwave Background (CMB) produced by the COBE, WMAP and Planck satellites. This signature, which consists in a missing of power with respect to that predicted by the ΛCDM model, might hint at a new cosmological phase before the standard inflationary era.The main point of this paper is taking into account the latest Planck polarisation data to investigate how the CMB polarisation improves the understanding of this feature. With this aim, we apply to the latest Planck data, both PR3 (2018) and PR4 (2020) releases, a new class of estimators capable of evaluating this anomaly by considering temperature and polarisation data both separately and in a jointly way. This is the first time that the PR4 dataset has been used to study this anomaly. To critically evaluate this feature, taking into account the residuals of known systematic effects present in the Planck datasets, we analyse the cleaned CMB maps using different combinations of sky masks, harmonic range and binning on the CMB multipoles.Our analysis shows that the estimator based only on temperature data confirms the presence of a lack of power with a lower-tail-probability (LTP), depending on the component separation method, ≤ 0.33% and ≤ 1.76% for PR3 and PR4, respectively. To our knowledge, the LTP≤ 0.33% for the PR3 dataset is the lowest one present in the literature obtained from Planck 2018 data, considering the Planck confidence mask. We find significant differences between these two datasets when polarisation is taken into account most likely due to a different level of systematics. Especially, the analysis with PR3 data, unlike that with PR4, seems to point towards a lack of power at large scales also for polarisation.Moreover, we also show that for the PR3 dataset the inclusion of the subdominant polarisation information provides estimates that are less likely accepted in a ΛCDM cosmological model than the only-temperature analysis over the entire harmonic-range considered. In particular, at ℓmax = 26, we found that no simulation has a value as low as the data for all the pipelines.

Finding origins of CMB anomalies in the inflationary quantum fluctuations

In this paper, we present compelling evidence for the parity asymmetry (a discrete symmetry separate from isotropy) in the Cosmic Microwave Background (CMB) map, measured through two-point temperature correlations. Any asymmetry associated with discrete symmetries, such as parity, challenges our understanding of quantum physics associated with primordial physics rather than LCDM (Λ Cold-Dark-Matter) itself. We commence by conducting a comprehensive analysis of the Planck CMB, focusing on the distribution of power in low-multipoles and temperature anticorrelations at parity conjugate points in position space. We find tension with the near scale-invariant power-law power spectrum of Standard Inflation (SI), with p-values of the order 𝒪(10-4 - 10-3). Alternatively, we explore the framework of direct-sum inflation (DSI), where a quantum fluctuation arises as a direct sum of two components evolving forward and backward in time at parity conjugate points in physical space. This mechanism results in a parity-asymmetric scale-dependent power spectrum, particularly prominent at low-multipoles, without any additional free model parameters. Our findings indicate that DSI is consistent with data on parity asymmetry, the absence of power at θ > 60°, and power suppression at low-even-multipoles which are major data anomalies in the SI model. Furthermore, we discover that the parameters characterizing the hemispherical power asymmetry anomaly become statistically insignificant when the large SI quadrupole amplitude is reduced to align with the data. DSI explains this low quadrupole with a p-value of 3.5%, 39 times higher than SI. Combining statistics from parameters measuring parity and low-ℓ angular power spectrum, we find that DSI is 50-650 times more probable than SI. In summary, our investigation suggests that while CMB temperature fluctuations exhibit homogeneity and isotropy, they also display parity-asymmetric behavior consistent with predictions of DSI. This observation provides a tantalizing evidence for the quantum mechanical nature of gravity.

Enhancing CMB map reconstruction and power spectrum estimation with convolutional neural networks

The accurate reconstruction of Cosmic Microwave Background (CMB) maps and the measurement of its power spectrum are crucial for studying the early universe. In this paper, we implement a convolutional neural network to apply the Wiener Filter to CMB temperature maps, and use it intensively to compute an optimal quadratic estimation of the power spectrum. Our neural network has a UNet architecture as that implemented in WienerNet, but with novel aspects such as being written in python 3 and TensorFlow 2. It also includes an extra channel for the noise variance map, to account for inhomogeneous noise, and a channel for the mask. The network is very efficient, overcoming the bottleneck that is typically found in standard methods to compute the Wiener Filter, such as those that apply the conjugate gradient. It scales efficiently with the size of the map, making it a useful tool to include in CMB data analysis. The accuracy of the Wiener Filter reconstruction is satisfactory, as compared with the standard method. We heavily use this approach to efficiently estimate the power spectrum, by performing a simulation-based analysis of the optimal quadratic estimator. We further evaluate the quality of the reconstructed maps in terms of the power spectrum and find that we can properly recover the statistical properties of the signal. We find that the proposed architecture can account for inhomogeneous noise efficiently. Furthermore, increasing the complexity of the variance map presents a more significant challenge for the convergence of the network than the noise level does.

A possible common explanation for several cosmic microwave background (CMB) anomalies: A strong impact of nearby galaxies on observed large-scale CMB fluctuations

Context. A new and hitherto unknown cosmic microwave background (CMB) foreground has recently been detected. A systematic decrease in CMB temperatures around nearby large spiral galaxies points to an unknown interaction with CMB photons in a sphere up to several projected megaparsecs around these galaxies. Aims. We investigate to what extent this foreground may impact the CMB fluctuation map and create the so-called CMB anomalies. Methods. Using the observed temperature decrements around the galaxies, and making some general assumptions about the unknown interaction, we propose a common radial temperature profile. By assigning this profile to nearby galaxies in the redshift range z = [0.004, 0.02], we created a foreground map model. Results. We find a remarkable resemblance between this temperature model map, based on nearby galaxies, and the Planck CMB map. Compared to 1000 simulated maps, we find that none of them show such a strong correlation with the foreground map over both large and small angular scales. In particular, the quadrupole, octopole, and ℓ = 4 and ℓ = 5 modes correlate with the foreground map to a high significance. Furthermore, one of the most prominent temperature decrements in the foreground map coincides with the position of the CMB cold spot. Conclusions. The largest scales of the CMB, and thereby the cosmological parameters, may change significantly after this foreground component is properly corrected. However, a reliable corrected CMB map can only be derived when suitable physical mechanisms are proposed and tested.

Delensing of Cosmic Microwave Background Polarization with Machine Learning

Primordial B-mode detection is one of the main goals of next-generation cosmic microwave background (CMB) experiments. Primordial B-modes are a unique signature of primordial gravitational waves (PGWs). However, the gravitational interaction of CMB photons with large-scale structures will distort the primordial E modes, adding a lensing B-mode component to the primordial B-mode signal. Removing the lensing effect (“delensing”) from observed CMB polarization maps will be necessary to improve the constraint of PGWs and obtain a primordial E-mode signal. Here, we introduce a deep convolutional neural network model named multi-input multi-output U-net (MIMO-UNet) to perform CMB delensing. The networks are trained on simulated CMB maps with size 20° × 20°. We first use MIMO-UNet to reconstruct the unlensing CMB polarization (Q and U) maps from observed CMB maps. The recovered E-mode power spectrum exhibits excellent agreement with the primordial EE power spectrum. The recovery of the primordial B-mode power spectrum for noise levels of 0, 1, and 2 μK-arcmin is greater than 98% at the angular scale of ℓ < 150. We additionally reconstruct the lensing B map from observed CMB maps. The recovery of the lensing B-mode power spectrum is greater than roughly 99% at the scales of ℓ > 200. We delens the observed B-mode power spectrum by subtracting the reconstructed lensing B-mode spectrum. The recovery of tensor B-mode power spectrum for noise levels of 0, 1, and 2 μK-arcmin is greater than 98% at the angular scales of ℓ < 120. Even at ℓ = 160, the recovery of tensor B-mode power spectrum is still around 71%.

Detection of Dipole Modulation in CMB Temperature Anisotropy Maps from WMAP and Planck using Artificial Intelligence

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.

Projected-field kinetic Sunyaev-Zel'dovich Cross-correlations: halo model and forecasts

The kinetic Sunyaev-Zel'dovich (kSZ) effect, i.e., the Doppler boost of cosmic microwave background (CMB) photons caused by their scattering off free electrons in galaxy clusters and groups with non-zero bulk velocity, is a powerful window on baryons in the universe. We present the first halo-model computation of the cross-power spectrum of the “projected-field” kSZ signal with large-scale structure (LSS) tracers. We compare and validate our calculations against previous studies, which relied on N-body-calibrated effective formulas rather than the halo model. We forecast results for CMB maps from the Atacama Cosmology Telescope (AdvACT), Simons Observatory (SO), and CMB-S4, and LSS survey data from the Dark Energy Survey, the Vera C. Rubin Observatory (VRO), and Euclid. In cross-correlation with galaxy number density, for AdvACT × unWISE we forecast an 18σ projected-field kSZ detection using data already in hand. Combining SO CMB maps and unWISE galaxy catalogs, we expect a 62σ detection, yielding precise measurements of the gas density profile radial slopes. Additionally, we forecast first detections of the kSZ — galaxy weak lensing cross-correlation with AdvACT × VRO/Euclid (at 6σ) and of the kSZ — CMB weak lensing cross-correlation with SO (at 16σ). Finally, ≈ 10-20% precision measurements of the shape of the gas density profile should be possible with CMB-S4 kSZ — CMB lensing cross-correlation without using any external datasets.

Velocity reconstruction with the cosmic microwave background and galaxy surveys

The kinetic Sunyaev Zel'dovich (kSZ) and moving lens effects, secondary contributions to the cosmic microwave background (CMB), carry significant cosmological information due to their dependence on the large-scale peculiar velocity field. Previous work identified a promising means of extracting this cosmological information using a set of quadratic estimators for the radial and transverse components of the velocity field. These estimators are based on the statistically anisotropic components of the cross-correlation between the CMB and a tracer of large scale structure, such as a galaxy redshift survey. In this work, we assess the challenges to the program of velocity reconstruction posed by various foregrounds and systematics in the CMB and galaxy surveys, as well as biases in the quadratic estimators. To do so, we further develop the quadratic estimator formalism and implement a numerical code for computing properly correlated spectra for all the components of the CMB (primary/secondary blackbody components and foregrounds) and a photometric redshift survey, with associated redshift errors, to allow for accurate forecasting. We create a simulation framework for generating realizations of properly correlated CMB maps and redshift binned galaxy number counts, assuming the underlying fields are Gaussian, and use this to validate a velocity reconstruction pipeline and assess map-based systematics such as masking. We highlight the most significant challenges for velocity reconstruction, which include biases associated with: modelling errors, characterization of redshift errors, and coarse graining of cosmological fields on our past light cone. Despite these challenges, the outlook for velocity reconstruction is quite optimistic, and we use our reconstruction pipeline to confirm that these techniques will be feasible with near-term CMB experiments and photometric galaxy redshift surveys.

Scaling transformations and the origins of light relics constraints from cosmic microwave background observations

We use here a family of scaling transformations, that scale key rates in the evolution equations, to analytically understand constraints on light relics from cosmic microwave background (CMB) maps, given cosmological models of varying degrees of complexity. We describe the causes of physical effects that are fundamentally important to the constraining power of the data, with a focus on the two that are most novel. We use as a reference model a cosmological model that admits a scaling transformation that increases light relic energy density while avoiding all of these causes. Constraints on light relics in a given model can then be understood as due to the differences between the given model and the reference model, as long as the additional light relics only interact gravitationally with the Standard Model components. This understanding supports the development of cosmological models that can evade light relics constraints from CMB maps.

Constraining cosmic inflation with observations: Prospects for 2030

ABSTRACT The ability to test and constrain theories of cosmic inflation will advance substantially over the next decade. Key data sources include cosmic microwave background (CMB) measurements and observations of the distribution of matter at low-redshift from optical, near-infrared, and 21-cm intensity surveys. A positive detection of a CMB B-mode consistent with a primordial stochastic gravitational wave background (SGWB) is widely viewed as a smoking gun for an inflationary phase. Still, a null result does not exclude inflation. However, in a significant class of inflationary scenarios, a low SGWB amplitude is correlated with a more significant running, αs, in the primordial density perturbations than is seen with the simplest inflationary potentials. With this motivation, we forecast the precision with which the spectral index ns and αs can be constrained by currently envisaged observations, including CMB (Simons Observatory, CMB-S4 and LiteBIRD), optical/near infra-red (DESI and SPHEREx), and 21-cm intensity mapping (Tianlai and CHIME) surveys. We identify optimal combinations of data sets for constraining the running and show that they may yield additional and informative constraints on the overall inflationary parameter space if the SGWB remains undetected.

QUIJOTE scientific results – VIII. Diffuse polarized foregrounds from component separation with QUIJOTE-MFI

ABSTRACT We derive linearly polarized astrophysical component maps in the Northern Sky from the QUIJOTE-MFI data at 11 and 13 GHz in combination with the Wilkinson Microwave Anisotropy Probe K and Ka bands (23 and 33 GHz) and all Planck polarized channels (30–353 GHz), using the parametric component separation method B-SeCRET. The addition of QUIJOTE-MFI data significantly improves the parameter estimation of the low-frequency foregrounds, especially the estimation of the synchrotron spectral index, βs. We present the first detailed βs map of the Northern Celestial Hemisphere at a smoothing scale of 2°. We find statistically significant spatial variability across the sky. We obtain an average value of −3.08 and a dispersion of 0.13, considering only pixels with reliable goodness of fit. The power-law model of the synchrotron emission provides a good fit to the data outside the Galactic plane but fails to track the complexity within this region. Moreover, when we assume a synchrotron model with uniform curvature, cs, we find a value of cs = −0.0797 ± 0.0012. However, there is insufficient statistical significance to determine which model is favoured, either the power law or the power law with uniform curvature. Furthermore, we estimate the thermal dust spectral parameters in polarization. Our cosmic microwave background, synchrotron, and thermal dust maps are highly correlated with the corresponding products of the PR4 Planck release, although some large-scale differences are observed in the synchrotron emission. Finally, we find that the βs estimation in the high signal-to-noise synchrotron emission areas is prior-independent, while, outside these regions, the prior governs the βs estimation.

Tracer-field cross-correlations with k-nearest neighbour distributions

ABSTRACT In astronomy and cosmology significant effort is devoted to characterizing and understanding spatial cross-correlations between points – e.g galaxy positions, high energy neutrino arrival directions, X-ray and AGN sources, and continuous fields – e.g. weak lensing meiand Cosmic Microwave Background maps. Recently, we introduced the k-nearest neighbour (kNN) formalism to better characterize the clustering of discrete (point) data sets. Here, we extend it to the point – field cross-correlations analysis. It combines kNN measurements of the point data set with measurements of the field smoothed at many scales. The resulting statistics are sensitive to all orders in the joint clustering of the points and the field. We demonstrate that this approach, unlike the 2-pt cross-correlation, can measure the statistical dependence of two data sets even when there are no linear (Gaussian) correlations between them. We further demonstrate that this framework is far more effective than the two point function in detecting cross-correlations when the continuous field is contaminated by high levels of noise. For a particularly high level of noise, the cross-correlation between haloes and the underlying matter field in a cosmological simulation, between 10 h−1 Mpc and 30 h−1 Mpc, is detected at &amp;gt;5σ significance using the technique presented here, when the two-point cross-correlation significance is ∼1σ. Finally, we show that kNN cross-correlations of haloes and the matter field can be well modelled on quasi-linear scales using the Hybrid Effective Field Theory (HEFT) framework, with the same set of bias parameters as are used for 2-pt cross-correlations. The substantial improvement in the statistical power of detecting cross-correlations using this method makes it a promising tool for various cosmological applications.

Level correlations of CMB temperature angular power spectrum

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