Planck 2018 results
Free Access
This article is an erratum for:

Volume 652, August 2021
Planck 2018 results
Article Number C4
Number of page(s) 3
Section Cosmology (including clusters of galaxies)
Published online 06 August 2021

In the original version, the bounds given in Eqs. (87a) and (87b) on the contribution to the early-time optical depth, τ(15, 30), contained a numerical error in deriving the 95th percentile from the Monte Carlo samples. The corrected 95% upper bounds are:



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 & Bouchet (2018) as was stated, but are instead comparable. Equations (1) and (2) give results that are now similar to those of Heinrich & 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.


We thank Xiaohan Wu for discussions which led to finding this error.


  1. Heinrich, C., & Hu, W. 2021, ArXiv e-prints [arXiv:2104.13998] [Google Scholar]
  2. Millea, M., & Bouchet, F. 2018, A&A, 617, A96 [CrossRef] [EDP Sciences] [Google Scholar]

© ESO 2021

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