# Riess, Casertano, Yuan, Bowers, Macri, Zinn, Scolnic — A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s⁻¹ Mpc⁻¹ Uncertainty (2021) **Adam G. Riess** and SH0ES team (Space Telescope Science Institute / Johns Hopkins University). arXiv:2012.08534, *ApJ* 908 L6 (2021) and follow-up *ApJ* 934 L7 (2022). (Paper uses Gaia EDR3 parallaxes combined with HST Cepheid photometry to calibrate $H_0$.) --- ## Overview The SH0ES team uses Gaia EDR3 parallaxes for 75 Milky Way Cepheids combined with HST spatial-scanning photometry to anchor the extragalactic distance ladder, yielding $H_0 = 73.2 \pm 1.3$ km s⁻¹ Mpc⁻¹. The paper explicitly marginalises over a global Gaia parallax zero-point offset, and finds **+14 µas residual** after applying the Lindegren EDR3 correction — i.e., the L21 correction **overcorrects** the Cepheid sample by 14 µas. This residual is the footprint of the sample-dependence of Gaia's zero point ([[2024_Ding_GalacticPlane_Parallax_Bias]], [[2025_Ding_Bright_Star_Parallax_Bias]]). The result is 4.2σ in tension with the Planck CMB value of $H_0$. --- ## PDF p.1 — Abstract (key numbers) ![[Riess2021_CepheidH0-001.png]] > "We find $H_0 = 73.2 \pm 1.3$ km s⁻¹ Mpc⁻¹, a 4.2σ difference with the prediction from Planck CMB observations under ΛCDM. We expect to reach ~1.3% precision in the near term from an expanded sample of ~40 SNe Ia in Cepheid hosts." --- ## PDF pp.3–11 — The Lindegren overcorrection ![[Riess2021_CepheidH0-003.png]] ![[Riess2021_CepheidH0-011.png]] From the SH0ES methodology: > "We find an indication of overcorrection of the parallax offset for Cepheids, with a median difference of 15 µas in the residuals" after applying Lindegren 2021. > [!critical] L21 overcorrects Cepheids by +14 to +15 µas > Riess et al. apply the official Lindegren EDR3 parallax correction to their 75 Cepheid sample and find a median residual of +14 µas (earlier 2021 paper reports +15 µas). Overcorrection means the published Gaia parallaxes, plus the Lindegren correction, are too small by 14–15 µas. If uncorrected, the Cepheid distances are systematically too large, which biases $H_0$ downward by a small but measurable amount. SH0ES compensates by marginalising over a global offset term. --- ## Why Cepheids need different PZPO than quasars - Cepheids are concentrated in the Galactic plane (where quasars are sparse). - Cepheids are bright (G < 11 mostly; quasars are G > 16). - Cepheids are variable stars (chromaticity changes with phase). Each of these factors takes Cepheids out of the regime where Lindegren's quasar-based correction is properly calibrated. The 14 µas residual is consistent with: - Ding 2024 galactic-plane offset of −31 µas vs L21's −17 µas. - Ding 2025 orbital-parallax bright-star offset of −39 µas. - Bobylev 2026 VLBI offset of −38 µas. > [!note] The +14 µas Cepheid residual fits the bright-star PZPO pattern > If the true bright-star Gaia PZPO is around −30 to −39 µas (as the bright-star cross-checks consistently find), but the L21 correction only applies −17 µas, then the residual is +13 to +22 µas. This is exactly what SH0ES measures at +14 µas. The Cepheid result is not an anomaly; it is a data point in the bright-star PZPO cluster. --- ## The Hubble-constant tension | Method | $H_0$ (km/s/Mpc) | |---|---| | SH0ES Cepheids + SNe Ia (this paper) | 73.2 ± 1.3 | | SH0ES 2022 follow-up | 73.04 ± 1.04 | | Planck CMB + ΛCDM | 67.4 ± 0.5 | | Tension | 4.2–5σ | The tension is "one of the most important open problems in cosmology" (widely quoted). --- ## Implications for the Gaia parallax calibration - If the Cepheid PZPO is actually −39 µas (Ding 2025) instead of −17 µas (Lindegren), the SH0ES Cepheid distances shrink by a small amount, which increases $H_0$ slightly. - Conversely if Riess is right about the Cepheids, then L21's global recipe is simply wrong for the Cepheid sample. - Either way, the Hubble-constant value depends on which PZPO the analyst chooses. - The ~1 km/s/Mpc uncertainty in $H_0$ maps to ~1% in distance, which is ~20 µas in parallax at 1 kpc — the same scale as the PZPO disagreements. --- ## Summary | Claim | Riess et al. (2021) | |---|---| | Lindegren EDR3 correction gives accurate Cepheid parallaxes | No. +14 µas residual — overcorrection. | | The Hubble constant tension is resolved | No. 4.2σ. | | $H_0$ is independent of Gaia PZPO choice | No. Explicitly marginalised over a global PZPO. | | Gaia EDR3 is a clean distance anchor for Cepheids | Not yet. Residual PZPO of ~15 µas exists in the Cepheid sample. | --- ## Citation Riess, A. G., Casertano, S., Yuan, W., Bowers, J. B., Macri, L., Zinn, J. C., Scolnic, D., 2021. "Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with ΛCDM." *Astrophysical Journal Letters* 908, L6. arXiv:2012.08534. Follow-up: Riess, A. G. et al., 2022. *ApJ* 934, L7. Local copy: . --- ## See also - [[2021_Lindegren_EDR3_Parallax_Bias]] - [[2024_Ding_GalacticPlane_Parallax_Bias]] - [[2025_Ding_Bright_Star_Parallax_Bias]] - [[2026_Bobylev_VLBI_Gaia_Zero_Point]] - [[2021_Groenewegen_Parallax_ZeroPoint_Offset]]