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Register a new userPlanck 2013 results. XXIII. Isotropy and statistics of the CMB
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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.
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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.
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.
We present the Planck likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations. We use this likelihood to derive the Planck CMB power spectrum over three decades in l, covering 2 <= l <= 2500. The main source of error at l <= 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher ls. For l < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz through a physically motivated Bayesian component separation technique. At l >= 50, we employ a correlated Gaussian likelihood approximation based on angular cross-spectra derived from the 100, 143 and 217 GHz channels. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on cosmological parameters. We find good internal agreement among the high-l cross-spectra with residuals of a few uK^2 at l <= 1000. We compare our results with foreground-cleaned CMB maps, and with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. The best-fit LCDM cosmology is in excellent agreement with preliminary Planck polarisation spectra. The standard LCDM cosmology is well constrained by Planck by l <= 1500. For example, we report a 5.4 sigma deviation from n_s /= 1. Considering various extensions beyond the standard model, we find no indication of significant departures from the LCDM framework. Finally, we report a tension between the best-fit LCDM model and the low-l spectrum in the form of a power deficit of 5-10% at l <~ 40, significant at 2.5-3 sigma. We do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent dataset. (Abridged)
Our velocity relative to the rest frame of the cosmic microwave background (CMB) generates a dipole temperature anisotropy on the sky which has been well measured for more than 30 years, and has an accepted amplitude of v/c = 0.00123, or v = 369km/s. In addition to this signal generated by Doppler boosting of the CMB monopole, our motion also modulates and aberrates the CMB temperature fluctuations (as well as every other source of radiation at cosmological distances). This is an order 0.1% effect applied to fluctuations which are already one part in roughly one hundred thousand, so it is quite small. Nevertheless, it becomes detectable with the all-sky coverage, high angular resolution, and low noise levels of the Planck satellite. Here we report a first measurement of this velocity signature using the aberration and modulation effects on the CMB temperature anisotropies, finding a component in the known dipole direction, (l,b)=(264, 48) [deg], of 384km/s +- 78km/s (stat.) +- 115km/s (syst.). This is a significant confirmation of the expected velocity.
The Planck design and scanning strategy provide many levels of redundancy that can be exploited to provide tests of internal consistency. One of the most important is the comparison of the 70GHz and 100GHz channels. Based on different instrument technologies, with feeds located differently in the focal plane, analysed independently by different teams using different software, and near the minimum of diffuse foreground emission, these channels are in effect two different experiments. The 143GHz channel has the lowest noise level on Planck, and is near the minimum of unresolved foreground emission. In this paper, we analyse the level of consistency achieved in the 2013 Planck data. We concentrate on comparisons between the 70/100/143GHz channel maps and power spectra, particularly over the angular scales of the first and second acoustic peaks, on maps masked for diffuse Galactic emission and for strong unresolved sources. Difference maps covering angular scales from 8deg-15arcmin are consistent with noise, and show no evidence of cosmic microwave background structure. Including small but important corrections for unresolved-source residuals, we demonstrate agreement between 70 and 100GHz power spectra averaged over 70<l<390 at the 0.8% level, and agreement between 143 and 100GHz power spectra of 0.4% over the same l range. These values are within and consistent with the overall uncertainties in calibration given in the Planck 2013 results. We also present results based on the 2013 likelihood analysis showing consistency at the 0.35% between the 100/143/217GHz power spectra. We analyse calibration procedures and beams to determine what fraction of these differences can be accounted for by known approximations or systematic errors that could be controlled even better in the future, reducing uncertainties still further. Several possible small improvements are described...(abridged)
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