We present here the Ðnal results of the Hubble Space T elescope (HST ) Key Project to measure the Hubble constant. We summarize our method, the results, and the uncertainties, tabulate our revised distances, and give the implications of these results for cosmology. Our results are based on a Cepheid calibration of several secondary distance methods applied over the range of about 60È400 Mpc. The analysis presented here beneÐts from a number of recent improvements and reÐnements, including (1) a larger LMC Cepheid sample to deÐne the Ðducial period-luminosity (PL) relations, (2) a more recent HST Wide Field and Planetary Camera 2 (WFPC2) photometric calibration, (3) a correction for Cepheid metallicity, and (4) a correction for incompleteness bias in the observed Cepheid PL samples. We adopt a distance modulus to the LMC (relative to which the more distant galaxies are measured) of mag, or 50 kpc. New, revised distances are given for the 18 spiral galaxies for k 0 (LMC) \ 18.50^0.10 which Cepheids have been discovered as part of the Key Project, as well as for 13 additional galaxies with published Cepheid data. The new calibration results in a Cepheid distance to NGC 4258 in better agreement with the maser distance to this galaxy. Based on these revised Cepheid distances, we Ðnd values (in km s~1 Mpc~1) of (random)^6 (systematic) (Type Ia supernovae),

Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation for its existence or magnitude. The acceleration of the Universe is, along with dark matter, the observed phenomenon that most directly demonstrates that our theories of fundamental particles and gravity are either incorrect or incomplete. Most experts believe that nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration. For these reasons, the nature of dark energy ranks among the very most compelling of all outstanding problems in physical science. These circumstances demand an ambitious observational program to determine the dark energy properties as well as possible.

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We present a new and independent determination of the local value of the Hubble constant based on a calibration of the tip of the red giant branch (TRGB) applied to Type Ia supernovae (SNe Ia). We find a value of H 0 = 69.8 ± 0.8 (±1.1% stat) ± 1.7 (±2.4% sys) km s−1 Mpc−1. The TRGB method is both precise and accurate and is parallel to but independent of the Cepheid distance scale. Our value sits midway in the range defined by the current Hubble tension. It agrees at the 1.2σ level with that of the Planck Collaboration et al. estimate and at the 1.7σ level with the Hubble Space Telescope (HST) SHoES measurement of H 0 based on the Cepheid distance scale. The TRGB distances have been measured using deep HST Advanced Camera for Surveys imaging of galaxy halos. The zero-point of the TRGB calibration is set with a distance modulus to the Large Magellanic Cloud of 18.477 ± 0.004 (stat) ± 0.020 (sys) mag, based on measurement of 20 late-type detached eclipsing binary stars, combined with an HST parallax calibration of a 3.6 μm Cepheid Leavitt law based on Spitzer observations. We anchor the TRGB distances to galaxies that extend our measurement into the Hubble flow using the recently completed Carnegie Supernova Project I ( CSP-I ) sample containing about 100 well-observed SNe Ia . There are several advantages of halo TRGB distance measurements relative to Cepheid variables; these include low halo reddening, minimal effects of crowding or blending of the photometry, only a shallow (calibrated) sensitivity to metallicity in the I band, and no need for multiple epochs of observations or concerns of different slopes with period. In addition, the host masses of our TRGB host-galaxy sample are higher, on average, than those of the Cepheid sample, better matching the range of host-galaxy masses in the CSP-I distant sample and reducing potential systematic effects in the SNe Ia measurements.

We describe observed properties of the Type Iax class of supernovae (SNe Iax), consisting of SNe observationally similar to its prototypical member, SN 2002cx. The class currently has 25 members, and we present optical photometry and/or optical spectroscopy for most of them. SNe Iax are spectroscopically similar to SNe Ia, but have lower maximum-light velocities (2000 |v| 8000 km s −1 ), typically lower peak magnitudes (−14.2 ≥ M V,peak −18.9 mag), and most have hot photospheres. Relative to SNe Ia, SNe Iax have low luminosities for their light-curve shape. There is a correlation between luminosity and light-curve shape, similar to that of SNe Ia, but offset from that of SNe Ia and with larger scatter. Despite a host-galaxy morphology distribution that is highly skewed to late-type galaxies without any SNe Iax discovered in elliptical galaxies, there are several indications that the progenitor stars are white dwarfs (WDs): evidence of C/O burning in their maximum-light spectra, low (typically ∼ 0.5 M ⊙ ) ejecta masses, strong Fe lines in their late-time spectra, a lack of X-ray detections, and deep limits on massive stars and star formation at the SN sites. However, two SNe Iax show strong He lines in their spectra. The progenitor system and explosion model that best fits all of the data is a binary system of a C/O WD that accretes matter from a He star and has a deflagration. At least some of the time, this explosion will not disrupt the WD. The small number of SNe in this class prohibit a detailed analysis of the homogeneity and heterogeneity of the entire class. We estimate that in a given volume there are 31 +17 −13 SNe Iax for every 100 SNe Ia, and for every 1 M ⊙ of iron generated by SNe Ia at z = 0, SNe Iax generate ∼0.036 M ⊙ . Being the largest class of peculiar SNe, thousands of SNe Iax will be discovered by LSST. Future detailed observations of SNe Iax should further our understanding of both their progenitor systems and explosions as well as those of SNe Ia.