<i>Planck</i> 2018 results

Abstract

In the original version, the bounds given in Eqs. (87a) and (87b) on the contribution to the early-time optical depth, (15,30), contained a numerical error in deriving the 95th percentile from the Monte Carlo samples. The corrected 95% upper bounds are: τ(15,30) &amp;lt; 0:018 (lowE, flat τ(15, 30), FlexKnot), (1) τ(15, 30) &amp;lt; 0:023 (lowE, flat knot, FlexKnot): (2) These bounds are a factor of 3 larger than the originally reported results. Consequently, the new bounds do not significantly improve upon previous results from Planck data presented in Millea &amp;amp; Bouchet (2018) as was stated, but are instead comparable. Equations (1) and (2) give results that are now similar to those of Heinrich &amp;amp; Hu (2021), who used the same Planck 2018 data to derive a 95% upper bound of 0.020 using the principal component analysis (PCA) model and uniform priors on the PCA mode amplitudes.

Keywords

Affiliated Institutions

• University of California, Berkeley US
• Université Paris Cité FR
• Jet Propulsion Laboratory US
• Institut National de Physique Nucléaire et de Physique des Particules FR
• Scuola Internazionale Superiore di Studi Avanzati IT
• University of Manchester GB
• Sorbonne Université FR
• University of Padua IT
• California Institute of Technology US
• AlbaNova SE
• Aix-Marseille Université FR
• University of Toronto CA
• Roche (France) FR
• Universidad de La Laguna ES
• Istituto Nazionale di Fisica Nucleare, Sezione di Bologna IT
• University of California, Davis US
• University of Oslo
• Laboratory for Ocean Physics and Satellite Remote Sensing FR
• European Space Astronomy Centre ES
• Sorbonne Paris Cité FR
• UNSW Sydney AU
• Indian Institute of Science Education and Research Thiruvananthapuram IN
• African Institute for Mathematical Sciences ZA
• Stellenbosch University ZA
• Centre National de la Recherche Scientifique FR
• Universidad de Oviedo ES
• Université de Bretagne Occidentale FR
• Laboratoire d’Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères FR
• Institut de Recherche pour le Développement FR
• Instituto de Física de Cantabria ES
• Helsinki Institute of Physics FI
• Institut d'Astrophysique Spatiale FR
• Istituto di Radioastronomia di Bologna IT
• Osservatorio Astronomico di Padova IT
• Ifremer FR
• National Institute of Science Education and Research IN
• Imperial College London GB
• Universidad de Cantabria ES
• University of Helsinki FI
• Istituto Nazionale di Fisica Nucleare, Sezione di Padova IT
• University of Sussex GB
• Université Paris-Saclay FR
• Cardiff University GB
• Trieste Astronomical Observatory IT
• Université Paris Sciences et Lettres FR
• École Normale Supérieure - PSL FR
• Commissariat à l'Énergie Atomique et aux Énergies Alternatives FR
• University of Ferrara IT
• Université Toulouse III - Paul Sabatier FR
• University of Milan IT
• Argonne National Laboratory US
• Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna IT
• Lawrence Berkeley National Laboratory US
• University of Cambridge GB
• Université Paris-Sud FR
• University of Geneva CH
• Shahid Beheshti University IR
• University of British Columbia CA
• Sun Yat-sen University CN
• University of KwaZulu-Natal ZA
• Leiden University NL
• Stockholm University SE
• Kavli Institute for the Physics and Mathematics of the Universe JP
• RWTH Aachen University DE
• University of the Western Cape ZA
• Simon Fraser University CA
• Université Grenoble Alpes FR
• Instituto de Astrofísica de Canarias ES
• Osservatorio di Astrofisica e Scienza dello Spazio
• Max Planck Institute for Astrophysics DE
• Institut d'Astrophysique de Paris FR
• National Centre for Nuclear Research PL
• Princeton University US
• Sapienza University of Rome IT
• Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara IT
• University of Warsaw PL
• The University of Tokyo JP
• Université Fédérale de Toulouse Midi-Pyrénées FR
• National Institute for Astrophysics IT

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