Planck 2015 results. XVI. Isotropy and statistics of the CMB (1506.07135v2)

Abstract: We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The "Cold Spot" is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.

• The paper confirms the Gaussianity of CMB temperature maps using skewness, kurtosis, and N-point correlation functions.
• It detects a ~7% dipolar asymmetry at the lowest multipoles via quadratic maximum likelihood and bipolar spherical harmonics methods.
• The analysis reveals low variance on large angular scales, challenging the standard assumptions of isotropic cosmology.

An Essay on Planck 2015 Results: Isotropy and Statistics of the CMB

The paper "Planck 2015 Results. XVI. Isotropy and Statistics of the CMB" presents a comprehensive examination of the statistical isotropy and Gaussianity of cosmic microwave background (CMB) anisotropies. Based on observations from the Planck satellite, the analysis is primarily concerned with temperature data from the full Planck mission, complemented by polarization measurements. The paper explores CMB anisotropy maps generated through various component-separation methods, investigating the underlying anomalies observed within these maps.

Core Findings

The analysis begins by confirming the absence of significant non-Gaussianity in the CMB temperature maps. Multiple statistical tools, including skewness, kurtosis, higher-order moments, and $N$-point correlation functions, were employed to probe these data sets, yielding results that are consistent with Gaussian expectations. In particular, skewness and kurtosis tests do not suggest deviations from Gaussianity. The examination of the 2-point correlation function and lack of correlation over large angular scales reaffirm known anomalies in the CMB, such as the lack of power at large scales, recognized by low map variance values.

The paper further assesses dipolar asymmetry within the CMB data. Using the quadratic maximum likelihood (QML) estimator and bipolar spherical harmonics (BipoSH), a dipole modulation in the CMB data is detected, revealing a slight asymmetry of approximately 7% across the sky. This asymmetry's direction aligns with findings from earlier analyses of the WMAP data, indicating its persistence across measurement campaigns. Moreover, dipolar modulation is predominately detected on scales corresponding to the lowest multipoles but does not extend to higher multipoles as strongly.

A variance-based anomaly is also discussed, particularly the unusually low variance affecting significant angular scales. When analyzed at lower resolutions, the variance consistently undershoots model predictions, suggesting an authentic feature of the observable universe rather than spurious noise or data artefact.

Implications and Theoretical Considerations

The detections of isotropy anomalies—both the lack of large-angle correlations and directional modulation—propose challenges to the standard model of cosmology which assumes a statistically isotropic universe. These findings have profound implications for our understanding of cosmic origins, potentially suggesting novel physics in the early universe or unrecognized influences on the foreground.

In addressing possible physical origins, theories such as those involving super-horizon reconciliations or exotic fields during inflation may be invoked. For instance, a detectable modulation or foreground contribution might imply traces of anisotropic expansion periods in the very early universe. Likewise, the CMB’s temperature variance discrepancy could emphasize a deeper energy distribution anomaly or non-standard early universe dynamics.

Future Directions

While the existing analysis robustly examines Planck’s primary mission data, the paper underscores an outlook towards further investigations involving polarization data and subsequent Planck data releases. Such data will elevate researchers' abilities to discern polarization-specific anomalies, effectively separating thermal CMB fluctuations from those anomalies induced by secondary effects like gravitational lensing or integrated Sachs-Wolfe effects.

Conclusion

The paper represents a crucial step in consolidating understanding around CMB isotropy, identifying isotropic and anisotropic features within the CMB, and testing the consistency of observed deviations against Gaussian cosmological models. Future inquiries should clarify these observations further, potentially harmonizing them with observations from other large-scale structure experiments and upgrading our grasp of the universe’s fundament.