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Register a new userPlanck 2018 results. VII. Isotropy and Statistics of the CMB
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Analysis of the Planck 2018 data set indicates that the statistical properties of the cosmic microwave background (CMB) temperature anisotropies are in excellent agreement with previous studies using the 2013 and 2015 data releases. In particular, they are consistent with the Gaussian predictions of the $Lambda$CDM cosmological model, yet also confirm the presence of several so-called anomalies on large angular scales. The novelty of the current study, however, lies in being a first attempt at a comprehensive analysis of the statistics of the polarization signal over all angular scales, using either maps of the Stokes parameters, $Q$ and $U$, or the $E$-mode signal derived from these using a new methodology (which we describe in an appendix). Although remarkable progress has been made in reducing the systematic effects that contaminated the 2015 polarization maps on large angular scales, it is still the case that residual systematics (and our ability to simulate them) can limit some tests of non-Gaussianity and isotropy. However, a detailed set of null tests applied to the maps indicates that these issues do not dominate the analysis on intermediate and large angular scales (i.e., $ell lesssim 400$). In this regime, no unambiguous detections of cosmological non-Gaussianity, or of anomalies corresponding to those seen in temperature, are claimed. Notably, the stacking of CMB polarization signals centred on the positions of temperature hot and cold spots exhibits excellent agreement with the $Lambda$CDM cosmological model, and also gives a clear indication of how Planck provides state-of-the-art measurements of CMB temperature and polarization on degree scales.
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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.
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.
This paper describes the 2018 Planck CMB likelihoods, following a hybrid approach similar to the 2015 one, with different approximations at low and high multipoles, and implementing several methodological and analysis refinements. With more realistic simulations, and better correction and modelling of systematics, we can now make full use of the High Frequency Instrument polarization data. The low-multipole 100x143 GHz EE cross-spectrum constrains the reionization optical-depth parameter $tau$ to better than 15% (in combination with with the other low- and high-$ell$ likelihoods). We also update the 2015 baseline low-$ell$ joint TEB likelihood based on the Low Frequency Instrument data, which provides a weaker $tau$ constraint. At high multipoles, a better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (polarization efficiency or PE) allow us to fully use the polarization spectra, improving the constraints on the $Lambda$CDM parameters by 20 to 30% compared to TT-only constraints. Tests on the modelling of the polarization demonstrate good consistency, with some residual modelling uncertainties, the accuracy of the PE modelling being the main limitation. Using our various tests, simulations, and comparison between different high-$ell$ implementations, we estimate the consistency of the results to be better than the 0.5$sigma$ level. Minor curiosities already present before (differences between $ell$<800 and $ell$>800 parameters or the preference for more smoothing of the $C_ell$ peaks) are shown to be driven by the TT power spectrum and are not significantly modified by the inclusion of polarization. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations. (Abridged)
The European Space Agencys Planck satellite, which was dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013, producing deep, high-resolution, all-sky maps in nine frequency bands from 30 to 857GHz. This paper presents the cosmological legacy of Planck, which currently provides our strongest constraints on the parameters of the standard cosmological model and some of the tightest limits available on deviations from that model. The 6-parameter LCDM model continues to provide an excellent fit to the cosmic microwave background data at high and low redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and polarization angular power spectra constrained well, Planck measures five of the six parameters to better than 1% (simultaneously), with the best-determined parameter (theta_*) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the LCDM model, and the connection to lower-redshift probes of structure formation. We also give a comprehensive summary of the major changes introduced in this 2018 release. The Planck data, alone and in combination with other probes, provide stringent constraints on our models of the early Universe and the large-scale structure within which all astrophysical objects form and evolve. We discuss some lessons learned from the Planck mission, and highlight areas ripe for further experimental advances.
We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter $Lambda$CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted base $Lambda$CDM in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density $Omega_c h^2 = 0.120pm 0.001$, baryon density $Omega_b h^2 = 0.0224pm 0.0001$, scalar spectral index $n_s = 0.965pm 0.004$, and optical depth $tau = 0.054pm 0.007$ (in this abstract we quote $68,%$ confidence regions on measured parameters and $95,%$ on upper limits). The angular acoustic scale is measured to $0.03,%$ precision, with $100theta_*=1.0411pm 0.0003$. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-$Lambda$CDM cosmology, the inferred late-Universe parameters are: Hubble constant $H_0 = (67.4pm 0.5)$km/s/Mpc; matter density parameter $Omega_m = 0.315pm 0.007$; and matter fluctuation amplitude $sigma_8 = 0.811pm 0.006$. We find no compelling evidence for extensions to the base-$Lambda$CDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be $N_{rm eff} = 2.99pm 0.17$, and the neutrino mass is tightly constrained to $sum m_ u< 0.12$eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -$Lambda$CDM at over $2,sigma$, which pulls some parameters that affect the lensing amplitude away from the base-$Lambda$CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)
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