In ΛCDM theory, a characteristic acoustic scale for the oscillating primordial photon and baryon plasma is established at the time of decoupling, when the plasma temperature has cooled sufficiently for recombination. Future GW source detections should provide tighter constraints. The most recent determination from the LIGO-Virgo-KAGRA Collaboration (2021) uses 47 gravitational wave sources from the Third LIGO-Virgo-KAGRA Gravitational Wave Transient Catalog, deriving a value of 68 -7 +12 km/s/Mpc. In this determination, the amplitude of gravitational waves resulting from the merger of a binary neutron star system are analyzed to determine the luminosity distance to the system, and a cosmological redshift obtained from optical identification of the source host galaxy. 2017), combined with collaborative followup observations identifying the optical counterpart of the source. The first estimate of the Hubble constant using a GW source detection was a joint effort of the LIGO/Virgo teams ( Abbott et al. Recent advances in gravitational wave (GW) detection technology provide an analysis approach independent of the cosmic distance ladder. They report an initial result of 71.0 ± 2.8(random) ± 2.1(systematic) km/s/Mpc. (2018) to derive H 0 from observations of H II galaxies and giant H II regions. Another standard candle method, based on the correlation between turbulent emission lines velocity dispersion and their integrated luminosity, is employed by Fernández Arenas et al. Characterization of potential systematics affecting the distance determination is a key issue in this method. entry, we plot the SH0ES result using Cepheids+SNIa only when combined with independent TRGB measures they derive a value of 72.53 ± 0.99. 2011), TRGB Dist Ladder ( Freedman et al. We represent determinations of this type with four entries in the first plot: the HST Key Project ( Freedman et al. Distances determined on cosmological scales rely on the 'distance ladder', which builds on the reliability of direct measurements close-by and the extension of those measurements outward through the use of standard candles such as Cepheid variables and Type Ia supernovae. The first determinations of H 0 involved measurements of distances and radial velocities associated with objects far enough away to not be bound gravitationally to our Local Group. The second plot compares determinations of H 0 through the use of only CMB data. Some measurements presented in this plot combine multiple datasets. This plot is designed to provide an overview of methods and tensions discussed in the literature. The first plot intercompares H 0 values derived from a variety of methods. We illustrate the recent history of Hubble constant determinations with two separate plots. Both unaccounted-for uncertainties in the data and potential inadequacy of the standard ΛCDM model may explain the tensions. However, a concordance value with associated uncertainty 1% or less has yet to be reached, and recent literature has noted the moderate tension between values for H 0 derived using a variety of methods. Current values in the literature hover near 70 km/s/Mpc. There are a number of reviews of this history we cite for example Freedman & Madore (2010), and online websites such as this one at CFA. There is a long history in the literature toward determination of an unbiased and accurate value of H 0, dating from the 1920's with the observations of galaxies by Hubble. The present-day (z=0) value of the expansion is referred to as the Hubble constant, H 0. Wei & Wu 2017, Chen, Kumar & Ratra 2017, Verde et al. The time-dependent expansion of spacetime is characterized in the FLRW equations as a function of redshift z by the Hubble parameter H(z).
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