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Planck 2018 Results. VI. Cosmological Parameters

Planck Collaboration

2020 · paper · Astronomy

Presents cosmological parameters from the final full-mission Planck measurements of the cosmic microwave background, using temperature, polarization and lensing. Finds good consistency with the standard six-parameter flat ΛCDM model, with a more precise reionization optical depth of 0.054.

Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.

13 findings

Substance Eq. (27) prints "Ωm = 0.3158 ± 0.0073" (68 %, TT,TE,EE+lowE+lensing), but the marginalized mean in Tables 1 and 2 is 0.3153 ± 0.0073; 0.3158 is the Table 1 best-fit value.

p. 24 Eq. (27)
Ωm = 0.3158 ± 0.0073
p. 15 Table 1, Ωm row
0.3153 ± 0.0073
p. 16 Table 2, TT,TE,EE+lowE+lensing
0.3153 ± 0.0073
p. 15 Table 1, Plik best fit / Plik[1]
0.3158

Judge's note: Eq. (27) on the p. 24 image reads 0.3158 ± 0.0073. Table 1 (p. 15) has best fit 0.3158 and mean 0.3153 ± 0.0073. Table 2 (p. 16), TT,TE,EE+lowE+lensing column, has 0.3153 ± 0.0073 and ΩΛ = 0.6847. The H0 in the same equation (67.36 ± 0.54) is the mean. So Eq. (27) attaches a marginalized error to the best-fit Ωm. The difference is small (0.0005).

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Substance Sect. 5.4 gives "our Planck TT,TE,EE+lowE+lensing estimate from Table 1 of H0 = (67.27 ± 0.60) km s−1Mpc−1"; Table 1 and Eq. (14) give 67.36 ± 0.54 for that combination, and 67.27 ± 0.60 is the TT,TE,EE+lowE (no lensing) value of Eq. (13) and Table 2.

p. 26 Sect. 5.4, first paragraph
Table 1 of H0 = (67.27 ± 0.60) km s−1Mpc−1
p. 15 Table 1, Plik [1] column, H0 row
67.36 ± 0.54
p. 16 Eq. (13), TT,TE,EE+lowE
H0 = (67.27 ± 0.60)
p. 26 Sect. 5.4, H0 discussion
our Planck TT,TE,EE+lowE+lensing estimate from Table 1 of H0 = (67.27 ± 0.60) km s−1Mpc−1

Only the authors can say what is right here.

Judge's note: Checked on the page images: p. 26 text; Table 1 on p. 15 (H0 67.36 ± 0.54); Eqs. (13) and (14) and Table 2 on p. 16. The label and the number disagree. The quoted 3.5σ tension holds with either value, so only the authors can say whether the label or the number was intended.

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Substance Conclusions (p. 62) define "S8 ≡ σ8Ωm^0.5 = 0.831 ± 0.013", leaving out the /0.3 normalisation used in the definition σ8(Ωm/0.3)^0.5 in Tables 1, 2 and Eq. (32).

p. 62 Conclusions, third bullet
S 8 ≡ σ8Ω0.5 m = 0.831 ± 0.013
p. 15 Table 1
S 8 ≡ σ8(Ωm/0.3)0.5
p. 62 Sect. 8 Conclusions, σ8 bullet
S 8 ≡σ8Ω0.5
p. 16 Table 2, row label
S 8 ≡σ8(Ωm/0.3)0.5

Judge's note: I checked the page images. Page 62 prints S8 ≡ σ8Ω^0.5_m with no /0.3. Table 1 (p. 15), Table 2 (p. 16) and Eq. (32) (p. 30) all print σ8(Ωm/0.3)^0.5. Under the printed Conclusions definition, the value would be σ8·sqrt(Ωm) ≈ 0.455, not 0.831. The squared forms are below because the arithmetic field allows no square roots.

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Substance The Fig. 35 caption quotes "H0 = (73.45 ± 1.66) km s−1Mpc−1 from Riess et al. (2018a)", while Sect. 5.4 says "R18 conclude that H0 = (73.48 ± 1.66) km s−1Mpc−1".

p. 49 Fig. 35 caption
(73.45 ± 1.66) km s−1Mpc−1 from Riess et al. (2018a)
p. 26 Sect. 5.4
R18 conclude that H0 = (73.48 ± 1.66) km s−1Mpc−1
p. 49 Fig. 35 caption
H0 = (73.45 ± 1.66) km s−1Mpc−1 from Riess et al. (2018a)
p. 26 Sect. 5.4
H0 = (73.48 ± 1.66) km s−1Mpc−1

Judge's note: Both images confirm the values. Both cite Riess et al. (2018a) for the same local H0 measurement with the same error, and no other version of R18 is mentioned. A search of the text finds 73.48 only in Sect. 5.4 and 73.45 only in the Fig. 35 caption. Sect. 5.4 is where the paper defines R18, so the caption's 73.45 is the likely slip.

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Substance Sect. 5.4 gives the inverse-distance-ladder result as "H0 = (67.9 ± 0.8) km s−1Mpc−1 and Ωm = 0.305 ± 0.001". An uncertainty of ±0.001 does not fit the red BAO+Pantheon+D/H BBN+θMC contour in Fig. 17.

p. 27 Sect. 5.4, text on Fig. 17
H0 = (67.9 ± 0.8) km s−1Mpc−1 and Ωm = 0.305 ± 0.001
p. 27 Sect. 5.4 text
Ωm = 0.305 ± 0.001
p. 27 Fig. 17, red contours
BAO+Pantheon+D/H BBN+θMC
p. 27 Sect. 5.4, discussion of Fig. 17
Ωm = 0.305 ± 0.001,

Only the authors can say what is right here.

Judge's note: I checked the p.27 text and Fig. 17. The red contours span about Ωm 0.28–0.33 at 95%, which suggests σ(Ωm) is about 0.01. The text also calls the result 'very close to' the full Planck likelihood, and that likelihood's Ωm error is several times larger than 0.001. The printed uncertainty looks like a dropped digit, but only the authors can give the correct value.

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Substance Sect. 6.2 reads "increasing the significance of AL > 1 to 2.8 σ (99.8 % of parameter samples have AL > 0, so the one-tailed limit is almost exactly 3 σ)". The threshold should be AL > 1.

p. 35 Sect. 6.2, right column
(99.8 % of pa-rameter samples have AL > 0, so the one-tailed limit is almost exactly 3 σ)
p. 35 Sect. 6.2, after Eq. (36)
99.8 % of parameter samples have AL > 0

Judge's note: The p.35 image prints 'AL > 0'. With AL = 1.180 ± 0.065, essentially every sample has AL > 0. The 99.8% fraction and the one-tailed ~3σ only make sense for the fraction of samples with AL > 1.

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Reference or label The Fig. 8 caption says "The impact of not including any of these corrections is shown in solid blue", but the legend shows '2018, None of these corrections' as solid red and solid blue as '2015 Planck TT,TE,EE+2018 lowE'.

p. 20 Fig. 8 caption and legend
The impact of not including any of these corrections is shown in solid blue
p. 20 Fig. 8 legend
2015 Planck TT,TE,EE+2018 lowE

Judge's note: The Fig. 8 legend on the p. 20 image has a red solid line for 'None of these corrections' and a blue solid line for 2015. The panels show both red and blue solid curves. The caption gives the wrong colour for the 'none' curve, and as worded it conflates that curve with the 2015 curve.

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Reference or label In Sect. 5.3, the GAMA data point is cited as "Galaxy and Mass Assembly (GAMA) redshift survey (Blake et al. 2012)", but the reference list's GAMA paper is Blake et al. 2013; Blake et al. 2012 is the WiggleZ paper.

p. 25 Sect. 5.3
Galaxy and Mass Assembly (GAMA) red-shift survey (Blake et al. 2012)
p. 25 Fig. 14 caption
dark red, GAMA (Blake et al. 2013)
p. 25 Sect. 5.3
shift survey (Blake et al. 2012). Two new surveys
p. 63 Reference list
Blake, C. et al., Galaxy And Mass Assembly (GAMA): improved cosmic growth

Judge's note: Sect. 5.3 on the p. 25 image cites Blake et al. 2012 for GAMA. The Fig. 14 caption on the same page cites GAMA as Blake et al. 2013 and WiggleZ as Blake et al. 2012. The p. 63 reference list has Blake 2012 = WiggleZ (MNRAS 425, 405) and Blake 2013 = GAMA (MNRAS 436, 3089).

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Reference or label Sect. 5.7 cites "Planck Collaboration XX 2016" for the 2015 cluster-count mass-bias analysis (0.58 ± 0.04, CMB-lensing mass calibration). In the reference list that entry is "Planck 2015 results. XX. Constraints on inflation".

p. 31 Sect. 5.7, before Eq. (34)
Planck Collaboration XX 2016 and Salvati et al. 2018). This
p. 31 after Eq. (34)
likelihood (Planck Collaboration XX 2016)
p. 67 Reference list
Planck Collaboration XX, Planck 2015 results. XX. Constraints on inﬂation.

Judge's note: The reference list (p.67) shows XX (2016) = constraints on inflation and XXIV (2016) = cosmology from SZ cluster counts. Sect. 5.7 itself attributes the 2015 cluster analysis to XXIV (2016). The XX (2016) citations on p.31 (before and after Eq. 34, and in the Zubeldia & Challinor paragraph) therefore point to the wrong paper. They should cite XXIV (2016).

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Reference or label Fig. 46 caption: "the 2σ preferred region suggested by the AMS proton excess (dashed ellipse)". The plot labels the dashed ellipse "AMS anti-proton excess", and the text says the same.

p. 61 Fig. 46 caption
suggested by the AMS proton excess (dashed ellipse)
p. 61 Sect. 7.9 text
AMS anti-proton excess
p. 61 Fig. 46 caption
preferred region suggested by the AMS proton excess (dashed ellipse)
p. 61 Fig. 46 label / text
The 95 % CL preferred region for the AMS anti-proton excess

Judge's note: The page 61 crops show the arrow to the dashed ellipse labelled "AMS anti-proton excess", while the caption says "AMS proton excess". The label in the caption is wrong.

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Wording Abstract states "in significant, 3.6 σ, tension with local measurements of the Hubble constant", whereas Sect. 5.4 gives "3.5 σ today (4.4 σ using Riess et al. 2019)" and the Introduction and Conclusions give 4.4σ; 3.6σ appears nowhere in the body.

p. 1 Abstract
in signiﬁcant, 3.6 σ, tension with local measurements of the Hubble constant
p. 26 Sect. 5.4
in 2013 to 3.5 σ today (4.4 σ using Riess et al. 2019)
p. 3 Introduction
at about the 4.4 σ level
p. 62 Conclusions
in substantial 4.4 σ ten-

Only the authors can say what is right here.

Judge's note: Viewed abstract (p1), Intro (p3), Sect. 5.4 (p26), Conclusions (p62). Grep finds 3.6σ only in the abstract (and an unrelated neutron-lifetime line). 3.5σ matches R18 (73.48±1.66) vs Table 1 67.36±0.54; 4.4σ matches Riess 2019 (74.03±1.42); 3.6σ is reproducible only with Riess 2018b (73.52±1.62, quoted on p26) but the paper never states that comparison. The data comparison behind the abstract figure is unstated; authors should say which local measurement and Planck combination the abstract uses.

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Wording Sect. 5.5 (p.29) reads "DES cosmic shear approximately constraining Ωmσ8^0.5 and CMB lensing constraining Ωmσ8^0.25", and Sect. 6.2 (p.37) reads "giving a value of Ωmσ8^0.25". Elsewhere the paper uses σ8Ωm^0.25 (Eq. 5) and S8 = σ8(Ωm/0.3)^0.5.

p. 29 Sect. 5.5, text on Fig. 19
constrain-ing Ωmσ0.5 8 and CMB lensing constraining Ωmσ0.25 8
p. 13 Eq. (5)
σ8Ω0.25 m = 0.589 ± 0.020
p. 29 Sect. 5.5
approximately constraining Ωmσ0.5 8 and CMB lensing constraining Ωmσ0.25 8
p. 37 Sect. 6.2
giving a value of Ωmσ0.25 8

Judge's note: On the page images (p.29 and p.37) the exponents are attached to σ8, not to Ωm, so this is not an extraction artefact. Eq. (5) defines the lensing combination as σ8Ωm^0.25. As printed, the text names a different parameter combination. The fix is to swap the exponents onto Ωm.

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Wording Sect. 7.6.2: "long-standing difference between neutrino lifetime measurements performed by beam and bottle experiments" should read "neutron lifetime".

p. 55 Sect. 7.6.2
standing diﬀerence between neutrino lifetime measurements performed by beam and bottle experiments
p. 55 Sect. 7.6.2
long- standing diﬀerence between neutrino lifetime measurements performed by beam and bottle experiments

Judge's note: Checked the page 55 crop. The same paragraph goes on to discuss the neutron lifetime τn and the PDG beam and bottle averages, so "neutrino" names the wrong particle.

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45 minor (typos and the like; most checked by the judge only)

Substance Conclusions quote "S8 ... = 0.831 ± 0.013" for the baseline Planck result, but Table 1 (Plik), Table 2 (TT,TE,EE+lowE+lensing) and Sect. 5.6 all give "0.832 ± 0.013".

p. 62 Conclusions
0.831 ± 0.013 is compatible with DES galaxy lensing
p. 15 Table 1 Plik column
0.832 ± 0.013
p. 30 Sect. 5.6
S 8 = 0.832 ± 0.013
p. 62 Sect. 8 Conclusions, σ8 bullet
0.831 ± 0.013

Judge's note: On p. 15, the Table 1 Plik column gives 0.832 ± 0.013 (best fit 0.8331; CamSpec 0.828; combined 0.830). On p. 16, Table 2 TT,TE,EE+lowE+lensing gives 0.832 ± 0.013. On p. 30, Sect. 5.6 says 'S8 = 0.832 ± 0.013'. The same Conclusions bullet quotes σ8 = 0.811 and Ωm = 0.315, which are the baseline values. No tabulated entry is 0.831, though recomputing from the rounded inputs gives about 0.831. The difference is small (0.001 against an error of 0.013).

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Reference or label Introduction: "quantified by the phenomenological AL parameter defined in Sect. 2.3" — AL is defined in Sect. 6.2 ("Lensing smoothing and AL"), not Sect. 2.3.

p. 3 Introduction, paragraph on tensions
phenomenological AL parameter deﬁned in Sect. 2.3
p. 3 Introduction
(quantiﬁed by the phenomenological AL parameter deﬁned in Sect. 2.3)
p. 3 Introduction, 2nd paragraph
quantiﬁed by the phenomenological AL parameter deﬁned in Sect. 2.3)
p. 35 Sect. 6.2
scaled by an “AL” consis-

Judge's note: Read Sect. 2.3 (pp12-14): it mentions AL only in the Fig. 3 caption and closing paragraph, each deferring to Sect. 6.2; the definition (theory lensing spectrum scaled by AL, expectation AL=1) is on p35, Sect. 6.2. Sect. 2.2.1 also points to 6.2. Pointer is loose rather than to a definition; minor.

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Reference or label Appendix A: "The differences listed in Table 1 can be seen visually in Fig. A.1". Fig. A.1 shows CamSpec TT, TE and EE constraints separately (the equivalent of Fig. 5), which matches Table A.1 rather than Table 1.

p. 69 Appendix A
The diﬀerences listed in Table 1 can be seen visually in Fig. A.1

Only the authors can say what is right here.

Judge's note: In the Appendix A text (p. 69), the previous paragraph discusses the TT/TE/EE differences between Table A.1 (CamSpec) and Table 2 (Plik). Table 1 compares only the combined TT,TE,EE+lowE+lensing results from Plik and CamSpec. Fig. A.1 is described as comparing parameters from TT, TE and EE separately using CamSpec. The pointer probably should be Table A.1, but Fig. A.1 also contains the combined result, so the authors should confirm.

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Wording Same TT,TE,EE+lowE result "AL = 1.180 ± 0.065, differing from unity by 2.7σ" (p9) vs "increasing the significance of AL > 1 to 2.8 σ" (p35).

p. 9 Sect. 2.2.1
AL = 1.180 ± 0.065, diﬀering from unity by 2.7σ
p. 35 Sect. 6.2 / Eq. (36b)
increasing the signiﬁcance of AL > 1 to 2.8 σ
p. 9 Sect. 2.2.1, end
differing from unity by 2.7σ

Judge's note: Both images confirm the same value and error for the baseline Plik TT,TE,EE+lowE likelihood. 0.180/0.065 = 2.77, which rounds to 2.8; the p9 figure appears truncated. Minor inconsistency.

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Wording "corresponding to a precise 0.05 % measurement of the angular scale" after Eq. (7), 100θ* = 1.04097 ± 0.00046, which is a 0.044 % precision.

p. 14 Sect. 3.1, after Eq. (7)
corresponding to a precise 0.05 % measurement of the angular scale
p. 14 after Eq. (7)
corresponding to a precise 0.05 % measurement of the angular

Only the authors can say what is right here.

Judge's note: Checked Eq. (7) and the following text on the p. 14 image. Both 0.00046/1.04097 and 0.00026/0.59643 come to about 0.044 %, which conventionally rounds to 0.04 %. Elsewhere on the page the paper rounds conventionally: 0.00030/1.04109 is called 0.03 % and the Eq. (10) relation is called 0.04 %. This is a minor imprecision in a wording-level percentage.

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Wording "gives a 0.05 % constraint on the combination" Ωm^0.3 h(Ωb h²)^-0.16 = 0.87498 ± 0.00052, which is a 0.059 % precision.

p. 14 Sect. 3.1, before Eq. (11)
gives a 0.05 % constraint on the combination

Only the authors can say what is right here.

Judge's note: Checked Eq. (11) on the p. 14 image. 0.00052/0.87498 comes to 0.059 %, which rounds to 0.06 %, not 0.05 %. Eq. (10), 0.036/101.056 = 0.036 %, is correctly called 0.04 %. This is a minor imprecision.

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Wording Conclusions: "There is some tension (at about 2.5 σ) with high-redshift BAO measurements from quasar Ly α observations". Sect. 5.1 instead gives 2.3σ for the superseded DR12 Lyα results, and says the newer DR14 result "lies within 1.7 σ of the Planck best-fit model".

p. 61 Conclusions, third bullet
There is some tension (at about 2.5 σ) with high-redshift BAO measurements from quasar Ly α observations
p. 23 Sect. 5.1
lies within 1.7 σ of the Planck best-ﬁt model
p. 61 Sect. 8 Conclusions, BAO bullet
There is some tension (at about 2.5 σ) with high-redshift
p. 23 Sect. 5.1
lies within 1.7 σ of the

Only the authors can say what is right here.

Judge's note: Page 23 says the DR12 combination was about 2.3σ low and was superseded by DR14 analyses within 1.7σ. Footnote 18 says the newer results are in closer agreement. Page 24 repeats "overall 2.3 σ tension" for the older results. Sect. 5.4 (text layer) says the model is "consistent with the most recent Ly α BAO measurements". No figure of 2.5σ appears in the body, so the summary in the Conclusions does not match the updated text. Only the authors can say which figure they intend.

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Wording Conclusions say DES clustering+lensing results "prefer a roughly 2.5 σ lower value of S8", but the S8 values in Sect. 5.6 (0.793 ± 0.024 for DES and 0.832 ± 0.013 for Planck) differ by about 1.4σ; Sect. 5.6 describes the tension as 'moderate (roughly 2 % PTE)' in the σ8–Ωm plane.

p. 62 Sect. 8 Conclusions
roughly 2.5 σ lower value of S 8
p. 30 Sect. 5.6, Eq. (32) and text
0.793 ± 0.024
p. 30 Sect. 5.6
moderate (roughly 2 % PTE)

Only the authors can say what is right here.

Judge's note: I checked Eq. (32) and the text below it on p. 30, and the Conclusions on p. 62. Sect. 5.6 gives the tension only as about 2% PTE in the 2D σ8–Ωm plane, not as a 2.5σ shift in S8. The naive 1D difference in S8 is about 1.4σ: the squared ratio below is about 2.04. The other mentions of 2.5σ in the paper refer to other datasets (KiDS/DES recalibration in Joudaki et al., clusters, BAO Lyα). Only the authors can say which statistic the 2.5σ refers to.

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Wording Sect. 7.6.2: "beam-only average gives τn = (888.0 ± 2.0) s, while the bottle-only average yields τn = (879.2 ± 0.6) s; these determinations are in 4.0 σ tension". Simple quadrature of the quoted errors gives about 4.2σ.

p. 55 Sect. 7.6.2
τn = (888.0 ± 2.0) s, while the bottle-only aver-age yields τn = (879.2 ± 0.6) s; these determinations are in 4.0 σ tension

Only the authors can say what is right here.

Judge's note: The page 55 image confirms the values. Adding the quoted errors in quadrature gives sqrt(4.00+0.36) ≈ 2.088, and 8.8/2.088 ≈ 4.21σ, compared with 4.0σ as printed. The paper does not say how the 4.0σ was computed; PDG scale factors or a different combination could explain it. The authors should be asked which method was used.

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Typo Abstract: "combining with data from BAO, BICEP2, and Keck Array data" repeats "data".

p. 1 Abstract
combining with data from BAO, BICEP2, and

Judge's note: Seen in abstract crop on p1. Redundant word; cosmetic.

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Typo Introduction p3: "including Type 1a supernovae" should be "Type Ia supernovae" (as in the abstract).

p. 3 Introduction
including Type 1a supernovae
p. 3 Introduction, paragraph on Sect. 5
Type 1a supernovae
p. 3 Introduction, layout paragraph
including Type 1a supernovae, redshift-space dis-

Judge's note: Page image shows the digit '1'; abstract uses 'Type Ia'.

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Typo PArthENoPE version given as "version 1.1 of the PArthENoPE BBN code" (Sect. 2.1, p4) but "version 1.10 of PArthENoPE" (Sect. 7.6.1, p52).

p. 4 Sect. 2.1
version 1.1 of the PArthENoPE BBN code (Pisanti et al. 2008, version 2.0 gives identical results)
p. 52 Sect. 7.6.1
version 1.10 of PArthENoPE40 (Pisanti et al. 2008)

Judge's note: Both images confirm the two forms. Likely the same release written two ways; harmonize.

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Typo "based only on Planck data and so does not including the WMAP" should be "does not include".

p. 11 Sect. 2.2.3
based only on Planck data and so does not including the WMAP
p. 11 Sect. 2.2.3, low-ℓ temperature likelihood
so does not including the WMAP

Judge's note: Confirmed on p11 image.

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Typo "The is due, at least in part, to the choice of how to model polarization efficiencies" should be "This is due".

p. 12 Sect. 2.2.5
The is due, at least in part, to
p. 12 Sect. 2.2.5, paragraph on AL and ΩK
The is due, at least in part,

Judge's note: Confirmed on p12 image.

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Typo "since it it probes much lower redshifts" — duplicated "it".

p. 12 Sect. 2.3
since it it probes much lower red-shifts
p. 12 Sect. 2.3
since it it probes much lower red-

Judge's note: Confirmed on p12 image; both words on one line.

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Typo "of which 8.3 ∆χ points are due to the improvement" — missing square; should be ∆χ².

p. 12 Sect. 2.2.5
of which 8.3 ∆χ points are due to the improve-ment
p. 12 Sect. 2.2.5
of which 8.3 ∆χ points are due to the improve-

Judge's note: Image p12 shows ∆χ without superscript while surrounding instances show ∆χ².

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Typo Stray word: "The constraints of Eq. (5) and (6) in are in very good agreement" (delete the first 'in').

p. 13 Text after Eq. (6)
The constraints of Eq. (5) and (6) in are in very good agreement
p. 13
The constraints of Eq. (5) and (6) in are in very

Judge's note: The page image (p. 13, right column after Eq. 6) shows 'Eq. (5) and (6) in are in very good agreement'. The first 'in' is superfluous.

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Typo "significantly more precise that those determined using TT alone" should read 'than'.

p. 14 Sect. 3, first paragraph
signiﬁcantly more precise that those determined using

Judge's note: The page image (p. 14, Sect. 3, first paragraph) shows 'more precise that those'. This is a plain typo for 'than'.

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Typo Misspelling: "F_AP is the Alcock-Paczinski parameter"; elsewhere, including the same page, the spelling is 'Alcock-Paczynski'.

p. 25 Text before Eq. (30)
FAP is the Alcock-Paczinski parameter
p. 23 Sect. 5.1
Alcock-Paczynski eﬀect, Alcock & Paczynski 1979

Judge's note: On the p. 25 image, the right column has 'Alcock-Paczynski effect' at the top and 'Alcock-Paczinski parameter' before Eq. (30). Sect. 5.1 and the reference also use 'Paczynski'.

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Typo "“consensus” BOSS D12 results from Alam et al. (2017)" should read 'DR12'.

p. 25 Sect. 5.3
sus” BOSS D12 results from Alam et al. (2017)
p. 25 Sect. 5.3
“consen- sus” BOSS D12 results
p. 25 Sect. 5.3
“consen-sus” BOSS D12 results from Alam et al. (2017)

Judge's note: Sect. 5.3 on the p. 25 image reads 'BOSS D12'. The same paragraph and the rest of the paper use 'DR12'.

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Typo Stray full stop in mid-sentence: "(sensitive to the Weyl potential, see Sect. 7.4). provides a test of General Relativity."

p. 25 Sect. 5.3
see Sect. 7.4). provides a test of General Relativity.

Judge's note: The p. 25 image, Sect. 5.3 first paragraph, shows '). provides', which breaks the sentence.

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Typo Footnote 20: "When using RSDs to constraint dark energy in Sect. 7.4" should read 'constrain'.

p. 25 footnote 20
When using RSDs to constraint dark energy in Sect. 7.4

Judge's note: Footnote 20 on the p. 25 image reads 'to constraint dark energy'.

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Typo "substantially lower that the distance-ladder estimate" should read 'than'.

p. 26 Sect. 5.4
substantially lower that the distance-ladder estimate
p. 26 Sect. 5.4
substantially lower that the

Judge's note: The p. 26 image, Sect. 5.4, reads 'substantially lower that the'.

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Typo Extra article: "possible systematic errors in the either the Planck or SH0ES data".

p. 26 Sect. 5.4
sible systematic errors in the either the Planck or SH0ES
p. 26 Sect. 5.4
possible systematic errors in the either the Planck or SH0ES

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Typo The Fig. 18 caption reads "Dark Energy Survey (DES) shear correlations functions"; it should read "correlation functions".

p. 29 Fig. 18 caption
Dark Energy Survey (DES) shear correlations functions

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Typo Sect. 5.7 reads "about 2 σ lower that the Planck CMB-lensing mass calibration"; 'that' should be 'than'.

p. 31 Sect. 5.7
lower that the Planck CMB-lensing mass calibration
p. 31 Sect. 5.7
is about 2 σ lower that the Planck CMB-lensing mass calibration

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Typo Sect. 5.7 reads "they find constraints the σ8–Ωm plane in tension"; the word 'in' is missing ('constraints in the σ8–Ωm plane').

p. 32
they ﬁnd constraints the σ8–Ωm plane in tension

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Typo The text after Eq. (35) reads "independent of the cosmological parameter fit to the ℓ ≥ 801 power spectra", but the split is defined as "ℓ ≤ 801 and ℓ ≥ 802".

p. 34 Text after Eq. (35)
independent of the cosmological pa-rameter ﬁt to the ℓ ≥ 801 power spectra
p. 32 Sect. 6.1
We consider the multipole ranges ℓ≤801 and ℓ≥802
p. 34 after Eq. (35)
parameter ﬁt to the ℓ≥801 power spectra
p. 32 Sect. 6.1
We consider the multipole ranges ℓ≤801 and

Judge's note: Seen on the images of p.32 (where the split is defined) and p.34. Eq. (35) uses ℓ ≤ 801, so the complementary range should be ℓ ≥ 802. This is a one-multipole slip.

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Typo Sect. 6.2 has an unmatched closing parenthesis in "because of the poorer agreement at ℓ < 1000)."

p. 36 Sect. 6.2
poorer agreement at ℓ< 1000). Varying AL allows

Judge's note: On p.36 the earlier parenthesis '(although in other multipole ranges it does not match at all)' is closed in a previous sentence. The sentence 'In ΛCDM the lensing amplitude ... at ℓ<1000).' has no opening parenthesis.

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Typo Sect. 6.2 reads "the low-ℓ polarization than constrains τ"; 'than' should be 'that'.

p. 37 Sect. 6.2
larization than constrains τ)

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Typo Sect. 7.1 reads "We have studied a range of extension to the base ΛCDM model."; it should read 'extensions'.

p. 37 Sect. 7.1
We have studied a range of extension to the base ΛCDM model.

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Typo Sect. 7.2.2: "provides a relative weak constraint on the tensor-to-scalar ratio" should read "relatively weak".

p. 38 Sect. 7.2.2
provides a relative weak constraint on the tensor-

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Typo Footnote 32: "The polarization anisotropies generated by gravitational waves was discussed first by Polnarev (1985)": the plural subject takes a singular verb ("was" should be "were").

p. 38 footnote 32
The polarization anisotropies generated by gravitational waves was discussed ﬁrst by Polnarev (1985).

Judge's note: Checked footnote 32 in the page 38 crop. The text is as quoted, and it is a subject–verb agreement slip.

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Typo Sect. 7.4.2: "Adding BAO/RSD + WL tightens the constrains (red contours)" should read "constraints".

p. 45 Sect. 7.4.2
Adding BAO/RSD + WL tightens the constrains (red contours)
p. 45 Sect. 7.4.2
tightens the constrains (red contours)

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Typo Sect. 7.5.1: "The 2018 lensing construction gives a slightly (1–2 %) higher lensing power spectrum amplitude" should probably read "lensing reconstruction".

p. 48 Sect. 7.5.1
The 2018 lensing construction gives a slightly (1–2 %) higher

Judge's note: In the page 48 crop, two sentences earlier the same paragraph says "the lensing reconstruction is very consistent with expected amplitudes". "construction" is very likely a dropped prefix, though the meaning is still clear.

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Typo Sect. 7.6.1: "about an order of magnitude smaller that the observational error" should read "smaller than".

p. 52 Sect. 7.6.1
about an order of magnitude smaller that the observational error

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Typo Sect. 7.6.1: "which we use in our joint fits of Planck+deutrium (D) data" should read "deuterium".

p. 54 Sect. 7.6.1, before Eq. (76)
Planck+deutrium (D) data
p. 54 Sect. 7.6.1, after A2 discussion
joint ﬁts of Planck+deutrium (D) data
p. 54
which we use in our joint ﬁts of Planck+deutrium (D) data

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Typo Sect. 7.6.2: "τn = [887 ± 1.2(stat.) ± 1.9(sys, )] s of Yue et al. (2013)" has stray punctuation, "(sys, )" for "(sys.)".

p. 55 Sect. 7.6.2
±1.9(sys, )] s of Yue et al. (2013)

Judge's note: The full page 55 image shows "1.9(sys, )] s", which is malformed punctuation.

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Typo Sect. 7.8: "PCA (principle-component analysis)" should read "principal-component analysis", as spelt in Sect. 7.7.

p. 57 Sect. 7.8, PCA bullet
PCA (principle-component analysis)
p. 56 Sect. 7.7
(often referred to as a principal-component analysis)
p. 57
PCA (principle-component analysis), which decomposes the

Judge's note: The page 57 crop shows "principle-component". The page 56 crop (Sect. 7.7) shows "principal-component analysis". This is a misspelling.

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Typo Sect. 7.8: "construct an approximate likelihood that can be convenient way of exploring other models" is missing an article ("a convenient way").

p. 58 Sect. 7.8, PCA bullet
it can be convenient way of exploring
p. 58
approximate likelihood that can be convenient way of exploring

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Typo Sect. 7.8: "the lensing amplitude can in-creased by increasing As" is missing "be" ("can be increased").

p. 60 Sect. 7.8
the lensing amplitude can in-creased by increasing As

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Typo Acknowledgements (p. 62) spell the name "Ignacy Sawicky"; the reference list spells it "Sawicki, I."

p. 62 Acknowledgements
Ignacy Sawicky

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that the acknowledged person is the I. Sawicki of the cited works (Bellini & Sawicki; Saltas et al.; Deffayet et al.). The page image shows 'Ignacy Sawicky' in the acknowledgements. The reference list consistently spells the name 'Sawicki, I.'

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Typo Conclusions (p. 62): "(ΩK = 0.0007 ± 0.0019), consistent the predictions of simple inflationary models" is missing 'with'.

p. 62 Sect. 8, primordial fluctuations bullet
consistent the pre-

Judge's note: The page image of p. 62, first bullet on primordial fluctuations, reads 'consistent the pre-/dictions'. The word 'with' is missing.

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Typo The reference list (p. 65) has two entries for the same work: "Heymans, C., Van Waerbeke, L., Miller, L., et al., CFHTLenS ... 2012, MNRAS, 427, 146, arXiv:1210.0032" and "Heymans, C. et al., CFHTLenS ... 2012, MNRAS, 427, 146, arXiv:1210.0032".

p. 65 Reference list
Heymans, C., Van Waerbeke, L., Miller, L., et al., CFHTLenS: the Canada-

Judge's note: The crop of p. 65 shows two consecutive entries with the same title, journal, volume, page and arXiv ID, and no a/b labels.

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Typo Fig. A.2 caption: "The red points in the upper panel panels show the 545 GHz-cleaned spectra" has a garbled duplicate word ('panel panels').

p. 72
The red points in the upper panel panels show the 545 GHz-cleaned spectra

Judge's note: The crop of the Fig. A.2 caption on p. 72 confirms 'upper panel panels' as printed. The same caption elsewhere uses 'upper panels'.

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