Abstract

Analysis of thePlanck2018 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 ΛCDM 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,QandU, or theE-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.,ℓ ≲ 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 ΛCDM cosmological model, and also gives a clear indication of howPlanckprovides state-of-the-art measurements of CMB temperature and polarization on degree scales.

Highlights

  • This paper, one of a set associated with the 2018 release of data from the Planck1 mission (Planck Collaboration I 2020), describes a compendium of studies undertaken to determine the statistical properties of both the temperature and polarization anisotropies of the cosmic microwave background (CMB).The ΛCDM model explains the structure of the CMB in detail (Planck Collaboration VI 2020), yet it remains entirely appropriate to look for hints of departures from, or tensions with, the standard cosmological model, by examining the statistical properties of the observed radiation

  • In polarization we find reasonable consistency with Monte Carlo (MC) simulations on intermediate and large angular scales, but there is a considerable range of p-values found, depending on the specific combinations of data considered

  • We show the separation angles and degrees of alignment between the preferred directions inferred from temperature, T, and E-mode polarization data, with the p-values measured as the fraction of simulations with separation angles smaller than those inferred from the data. (a)α is the separation angle between the preferred directions computed for the temperature and E-mode polarization data

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Summary

Isotropy and statistics of the CMB

Planck Collaboration: Y. Akrami14,49,51, M. Ashdown58,5, J. Aumont85, C. Baccigalupi68, M. Ballardini20,36, A. J. Banday85,8, , R. B. Barreiro53, N. Bartolo25,54, S. Basak75, K. Benabed48,84, M. Bersanelli28,40, P. Bielewicz67,66,68, J. J. Bock55,10, J. R. Bond7, J. Borrill12,82, F. R. Bouchet48,79, F. Boulanger78,47,48, M. Bucher2,6, C. Burigana39,26,42, R. C. Butler36, E. Calabrese72, J.-F. Cardoso48, B. Casaponsa53, H. C. Chiang22,6, L. P. L. Colombo28, C. Combet60, D. Contreras19, B. P. Crill55,10, P. de Bernardis27, G. de Zotti37, J. Delabrouille2, J.-M. Delouis48,84, E. Di Valentino56, J. M. Diego53, O. Doré55,10, M. Douspis47, A. Ducout59, X. Dupac31, G. Efstathiou58,50, F. Elsner63, T. A. Enßlin63, H. K. Eriksen51, Y. Fantaye3,18, R. Fernandez-Cobos53, F. Finelli36,42, M. Frailis38, A. A. Fraisse22, E. Franceschi36, A. Frolov77, S. Galeotta38, S. Galli57, K. Ganga2, R. T. Génova-Santos52,15, M. Gerbino83, T. Ghosh71,9, J. González-Nuevo16, K. M. Górski55,86, , A. Gruppuso36,42, J. E. Gudmundsson83,22, J. Hamann76, W. Handley58,5, F. K. Hansen51, D. Herranz53, E. Hivon48,84, Z. Huang73, A. H. Jaffe46, W. C. Jones22, E. Keihänen21, R. Keskitalo12, K. Kiiveri21,35, J. Kim63, N. Krachmalnicoff68, M. Kunz13,47,3, H. Kurki-Suonio21,35, G. Lagache4, J.-M. Lamarre78, A. Lasenby5,58, M. Lattanzi26,43, C. R. Lawrence55, M. Le Jeune2, F. Levrier78, M. Liguori25,54, P. B. Lilje51, V. Lindholm21,35, M. López-Caniego31, Y.-Z. Ma56,70,65, J. F. Macías-Pérez60, G. Maggio38, D. Maino28,40,44, N. Mandolesi36,26, A. Mangilli8, A. Marcos-Caballero53, M. Maris38, P. G. Martin7, E. Martínez-González53, , S. Matarrese25,54,33, N. Mauri42, J. D. McEwen64, P. R. Meinhold23, A. Mennella28,40, M. Migliaccio30,45, M.-A. Miville-Deschênes1,47, D. Molinari26,36,43, A. Moneti48, L. Montier85,8, G. Morgante36, A. Moss74, P. Natoli26,81,43, L. Pagano47,78, D. Paoletti36,42, B. Partridge34, F. Perrotta68, V. Pettorino1, F. Piacentini27, G. Polenta81, J.-L. Puget47,48, J. P. Rachen17, M. Reinecke63, M. Remazeilles56, A. Renzi54, G. Rocha55,10, C. Rosset2, G. Roudier2,78,55, J. A. Rubiño-Martín52,15, B. Ruiz-Granados52,15, L. Salvati47, M. Savelainen21,35,62, D. Scott19, E. P. S. Shellard11, C. Sirignano25,54, R. Sunyaev63,80, A.-S. Suur-Uski21,35, J. A. Tauber32, D. Tavagnacco38,29, M. Tenti41, L. Toffolatti16,36, M. Tomasi28,40, T. Trombetti39,43, L. Valenziano36, J. Valiviita21,35, B. Van Tent61, P. Vielva53, , F. Villa36, N. Vittorio30, B. D. Wandelt48,84,24, I. K. Wehus51, A. Zacchei38, J. P. Zibin19, and and A. Zonca69

Introduction
Polarization analysis preamble
Data description
Simulations
E B polarization
Tests of non-Gaussianity
One-dimensional moments
N-point correlation functions
Minkowski functionals
Peak statistics
Non-oriented stacking
Oriented stacking
Anomalies in the microwave sky
Lack of large-angle correlations
Hemispherical asymmetry
Method
Peak distribution asymmetry
The Cold Spot and other large-scale peaks in temperature and polarization
Dipole modulation and directionality
Variance asymmetry
Dipole modulation
Angular clustering of the power distribution
Conclusions
Introduction and notation
Masking
Overview
Finite-difference stencils
Multigrid methods
Method description
Performance considerations
Findings
Reconstruction residuals and confidence mask
Full Text
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