Planck 2013 results. XXIII. Isotropy and statistics of the CMB

TL;DR

Planck 2013 XXIII tests the statistical isotropy and Gaussianity of the CMB using Planck data, including multiple component-separation maps and extensive simulations. The results broadly support Gaussian isotropy but reveal large-scale anomalies such as a deficit of power at low multipoles, a low CMB variance, quadrupole–octopole alignment, hemispherical and dipolar power asymmetries, and phase correlations. The bispectrum shows no significant primordial non-Gaussianity beyond secondary effects, while phenomenological models like dipole modulation (BipoSH) capture several large-scale features but none comprehensively explain all anomalies. These findings have potential implications for low-ℓ cosmology and parameter estimation, underscoring the value of polarization data to distinguish cosmological signals from systematics or foregrounds.

Abstract

The two fundamental assumptions of the standard cosmological model - that the initial fluctuations are statistically isotropic and Gaussian - are rigorously tested using maps of the cosmic microwave background (CMB) anisotropy from the Planck satellite. Deviations from isotropy have been found and demonstrated to be robust against component separation algorithm, mask choice and frequency dependence. Many of these anomalies were previously observed in the WMAP data, and are now confirmed at similar levels of significance (about 3 sigma). However, we find little evidence for non-Gaussianity, with the exception of a few statistical signatures that seem to be associated with specific anomalies. In particular, we find that the quadrupole-octopole alignment is also connected to a low observed variance of the CMB signal. A power asymmetry is now found to persist to scales corresponding to about l=600, and can be described in the low-l regime by a phenomenological dipole modulation model. However, any primordial power asymmetry is strongly scale-dependent and does not extend to arbitrarily small angular scales. Finally, it is plausible that some of these features may be reflected in the angular power spectrum of the data, which shows a deficit of power on similar scales. Indeed, when the power spectra of two hemispheres defined by a preferred direction are considered separately, one shows evidence for a deficit in power, while its opposite contains oscillations between odd and even modes that may be related to the parity violation and phase correlations also detected in the data. Although these analyses represent a step forward in building an understanding of the anomalies, a satisfactory explanation based on physically motivated models is still lacking.

Figures (43)

• Figure 1: Variance, skewness, and kurtosis for the combined map of the four different component separation methods. From top row to bottom row C-R, NILC, SEVEM, SMICA.
• Figure 2: $N$-pdf $\chi^2$ for the U73 mask, CL58, CL37, ecliptic North and ecliptic South. The different colours represent the four component separation methods, namely C-R (green), NILC (blue), SEVEM (red), and SMICA (orange).
• Figure 3: Frequency dependence for 70GHz (green), 100GHz (blue), 143GHz (red), and 217GHz (orange), for different masks.
• Figure 4: Two sets of discs of radius 10∘$^\circ$ A (top) and B (middle), for the $N_{\rm side}=512$ CMB estimates; and a set of 20 randomly placed discs of radius 3∘$^\circ$ super-imposed on the U73 mask (blue region) for the CMB estimates at $N_{\rm side}=2048$ (bottom).
• Figure 5: Pseudo-collapsed 3-point function averaged over disc set A for the raw (upper figure) and SEVEM foreground corrected (lower figure) 143GHz map at $N_{\rm side}=512$ for different values of sky coverage ($f_{\rm sky}$). Estimates of the multipoles for $\ell \leq 18$ are removed from the sky maps. The black solid line indicates the mean for 1000 MC simulations and the shaded dark and light grey regions indicate the 68% and 95% confidence regions, respectively, for the CG90 ($f_{\rm sky}=0.9$) mask. See Sect. \ref{['sec:npoint_correlation']} for the definition of the separation angle $\theta$.