Planck 2018 results
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Table 2.

Parameter constraints for different lensing datasets and priors, with and without galaxy BAO data.

ΛCDM
ΛCDM + ∑mν
Lensing
Lensing+BAO
Lensing
Lensing+BAO
σ8 H0 Ωm σ8 Σmν [eV]
MV conservative 8 ≤ L ≤ 400....... 0.589 ± 0.020 0.811 ± 0.019 0.569 ± 0.023 0.730 ± 0.041
DES lensing joint....... 0.599 ± 0.018 0.805 ± 0.014 67.6 ± 1.0 0.295 ± 0.011 0.586 ± 0.019
DES combined joint....... 0.589 ± 0.014 0.799 ± 0.013 67.1 ± 1.0 0.286 ± 0.009 0.576 ± 0.015 0.748 ± 0.028
100θMC = 1.0409 ± 0.0006 joint....... 0.592 ± 0.020 0.812 ± 0.015 68.0 ± 0.7 0.304 ± 0.009 0.570 ± 0.022
Planck TT+lowE joint....... 0.609 ± 0.008 0.809 ± 0.006 67.5 ± 0.5 0.311 ± 0.007 < 0.063
Planck TT,TE,EE+lowE joint....... 0.608 ± 0.006 0.810 ± 0.006 67.7 ± 0.4 0.311 ± 0.006 < 0.058

MV conservative 40 ≤ L ≤ 400....... 0.588 ± 0.021 0.813 ± 0.020 0.569 ± 0.024 0.729 ± 0.041
MV aggressive 8 ≤ L ≤ 425....... 0.591 ± 0.019 0.813 ± 0.019 0.573 ± 0.023 0.736 ± 0.039
MV aggressive 8 ≤ L ≤ 2048....... 0.578 ± 0.016 0.797 ± 0.016 67.4 ± 1.1 0.559 ± 0.018
TT conservative 8 ≤ L ≤ 400....... 0.572 ± 0.022 0.803 ± 0.021 0.553 ± 0.023
TT aggressive 8 ≤ L ≤ 2048....... 0.786 ± 0.017 66.4 ± 1.1 0.275 ± 0.014 0.541 ± 0.018
CompSep mask 8 ≤ L ≤ 400....... 0.591 ± 0.020 0.812 ± 0.019 0.572 ± 0.023 0.735 ± 0.040

DES priors....... 0.591 ± 0.020 0.586 ± 0.020 0.775 ± 0.030
″ + (Ωbh2 = 0.0222 ± 0.0005)....... 0.593 ± 0.020 68.0 ± 1.5 0.306 ± 0.022 0.586 ± 0.020
Best-fit ....... 0.586 ± 0.020 0.806 ± 0.019 0.566 ± 0.023 0.726 ± 0.041
″ (MV aggressive 8 ≤ L ≤ 2048)....... 0.575 ± 0.016 0.793 ± 0.016 67.6 ± 1.1 0.557 ± 0.018
Takahashi halofit....... 0.587 ± 0.020 0.809 ± 0.020 0.560 ± 0.025 0.720 ± 0.044
″ (MV aggressive 8 ≤ L ≤ 2048)....... 0.574 ± 0.017 0.795 ± 0.017 67.3 ± 1.1 0.548 ± 0.020
Linear theory....... 0.597 ± 0.020 0.820 ± 0.020 0.578 ± 0.024 0.742 ± 0.042

Notes. The top block shows parameter constraints using the default conservative Planck lensing likelihood, alone and in combination with the DES lensing likelihood, the DES combined lensing and galaxy clustering likelihood, the Planck CMB acoustic scale, as well as the full Planck CMB power spectra. The middle block shows results for lensing alone when changing the lensing multipole range, using only temperature reconstruction (TT) rather than the minimum-variance combination with polarization (MV), or changing the binning scheme. In this context, “conservative” and “aggressive” refer to the individual bin boundaries listed in the upper and lower parts, respectively, of Table 1, so that, for instance, “MV aggressive 8 ≤ L ≤ 425” uses the first nine bins in the lower part of that table. The “CompSep mask” row shows results when constructing the lensing mask using the final common mask from Planck Collaboration IV (2020), rather than the earlier SMICA mask used by default throughout this paper. The lower block gives results from the default conservative (or aggressive) lensing likelihood when varying assumptions. The best-fit row shows the result of using a fixed ΛCDM fit to Planck TT,TE,EE+lowE for the CMB power spectra (as in the 2015 analysis) rather than marginalizing out the theoretical CMB spectra. The two “DES prior” rows (following DES Collaboration 2018b) use flat priors on 0.1 <  Ωm <  0.9, 0.03 <  Ωb <  0.07, 0.87 <  ns <  1.07, 0.55 <  h <  0.91, 0.5 <  109As <  5, and, when varying neutrino mass, 0.05 eV <  ∑mν <  1 eV (which is then unconstrained over this interval). All other results use flat priors on 0.001 <  Ωch2 <  0.99, 0.5 <  θMC <  10, 1.61 <  log(1010As) < 3.91 and (except when combined with Planck CMB power spectra) our default lensing priors of 0.4 <  h <  1, ns = 0.96 ± 0.02, Ωbh2 = 0.0222 ± 0.0005; when varying the neutrino mass, the flat prior is ∑mν <  5 eV with three degenerate neutrinos. Note these prior sensitivities have no impact on joint constraints with the CMB power spectra, where the lensing likelihood can be calculated self-consistently without additional priors. The small sensitivity to nonlinear modeling is demonstrated by using the Takahashi et al. (2012) variant of the halofit nonlinear model (Smith et al. 2003) rather than the default HMcode (Mead et al. 2016), and by comparison to the linear theory result when the nonlinear corrections are entirely neglected. All limits in this table are 68% intervals, and H0 is in units of km s−1 Mpc−1.

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