A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s-1 Mpc-1 Uncertainty from the Hubble Space Telescope and the SH0ES Team

We report observations from the Hubble Space Telescope (HST) of Cepheid variables in the host galaxies of 42 Type Ia supernovae (SNe Ia) used to calibrate the Hubble constant (H ₀). These include the complete sample of all suitable SNe Ia discovered in the last four decades at redshift z ≤ 0.01, collected and calibrated from ≥1000 HST orbits, more than doubling the sample whose size limits the precision of the direct determination of H ₀. The Cepheids are calibrated geometrically from Gaia EDR3 parallaxes, masers in NGC 4258 (here tripling that sample of Cepheids), and detached eclipsing binaries in the Large Magellanic Cloud. All Cepheids in these anchors and SN Ia hosts were measured with the same instrument (WFC3) and filters (F555W, F814W, F160W) to negate zero-point errors. We present multiple verifications of Cepheid photometry and six tests of background determinations that show Cepheid measurements are accurate in the presence of crowded backgrounds. The SNe Ia in these hosts calibrate the magnitude-redshift relation from the revised Pantheon+ compilation, accounting here for covariance between all SN data and with host properties and SN surveys matched throughout to negate systematics. We decrease the uncertainty in the local determination of H ₀ to 1 km s^-1 Mpc^-1 including systematics. We present results for a comprehensive set of nearly 70 analysis variants to explore the sensitivity of H ₀ to selections of anchors, SN surveys, redshift ranges, the treatment of Cepheid dust, metallicity, form of the period-luminosity relation, SN color, peculiar-velocity corrections, sample bifurcations, and simultaneous measurement of the expansion history. Our baseline result from the Cepheid-SN Ia sample is H ₀ = 73.04 ± 1.04 km s^-1 Mpc^-1, which includes systematic uncertainties and lies near the median of all analysis variants. We demonstrate consistency with measures from HST of the TRGB between SN Ia hosts and NGC 4258, and include them simultaneously to yield 72.53 ± 0.99 km s^-1 Mpc^-1. The inclusion of high-redshift SNe Ia yields H ₀ = 73.30 ± 1.04 km s^-1 Mpc^-1 and q ₀ = -0.51 ± 0.024. We find a 5σ difference with the prediction of H ₀ from Planck cosmic microwave background observations under ΛCDM, with no indication that the discrepancy arises from measurement uncertainties or analysis variations considered to date. The source of this now long-standing discrepancy between direct and cosmological routes to determining H ₀ remains unknown.