Hubble Constant
The Hubble constant (H0) is the constant of proportionality in Hubble's law, which states that the redshift of a distant galaxy increases in proportion to its distance. It is quoted in kilometres per second per megaparsec, and in standard cosmology it is read as the present-day rate of expansion of the universe.
The redshift–distance relation was published by Edwin Hubble in 1929, building on radial-velocity measurements made by Vesto Slipher from 1912 onward and on Hubble's own Cepheid distances; Georges Lemaître had derived essentially the same relation from theory two years earlier. Hubble's original slope was about 500 km/s/Mpc, which implied an age for the universe smaller than the known age of the Earth — an embarrassment resolved only when the distance scale was repeatedly revised downward over the following decades. Modern values are near 70 km/s/Mpc. The reciprocal of H0, the Hubble time, is about 14 billion years for that value, and is the origin of the familiar figure for the age of the universe.
The Hubble tension
There is a real and unresolved conflict here, and it should not be understated. Measurements that build outward from nearby distance indicators — Cepheid variables calibrating Type Ia supernovae, as in the SH0ES programme — give values around 73 km/s/Mpc. Values inferred instead from the angular power spectrum of the Cosmic Microwave Background, notably by the Planck satellite, give about 67 km/s/Mpc. The quoted uncertainties on both are small enough that the discrepancy is several standard deviations, and a decade of work has failed to make it go away. Independent methods — the tip of the red giant branch, gravitational lensing time delays, and more recently JWST observations of Cepheids — have been marshalled on both sides without settling it.
Within the standard framework the tension is a parameter problem: either one of the measurements has an unrecognised systematic error, or the concordance model needs modification in the early universe. Outside that framework it is read as a symptom of the interpretation itself.
On this wiki
The researchers catalogued here mostly deny that H0 measures an expansion rate at all, and instead treat it as a measure of how much energy light loses per unit distance travelled. Related material is under Category:Redshift and Category:Cosmology.
H0 as a photon energy-loss rate. Lyndon Ashmore's "new tired light" derives the Hubble constant directly from the density of free electrons in intergalactic space, in Recoil Interaction Between Photons and The Electrons In The Plasma Of Intergalactic Space Leading To The Hubble Constant And CMB and An Explanation of Redshifts In a Static Universe. On this reading the same number that cosmologists call an expansion rate is a property of the intervening medium, and the quantity is a constant of space, not of time. Ari Brynjolfsson's plasma redshift work makes a comparable claim. See Tired Light for the general class of models.
Is it constant? Jean Pierre Vigier, Toivo Jaakkola and Jean-Claude Pecker argued in Spatial Fluctuation of the Hubble "Constant" that the measured value varies from one direction and region of sky to another — which, if true, is fatal to reading it as a global expansion rate but quite natural if it reflects the properties of intervening matter. Halton Arp's Seeing Red: Redshifts, Cosmology and Academic Science makes the more radical claim that a component of redshift is intrinsic to the object and unrelated to distance at all, which would corrupt the distance calibration on which H0 rests.
Alternative frameworks that reproduce Hubble's law. Tuomo Suntola's Dynamic Universe derives the observed magnitude–redshift relation without dark energy in Observations Support Spherically Closed Dynamic Space Without Dark Energy. C Johan Masreliez's Scale Expanding Cosmos Theory I – An introduction reinterprets the relation as an effect of changing scale rather than recession. Bob Ticer's The Recycling Universe and Grote Reber and Paul Marmet's Cosmic Matter and the Nonexpanding Universe pursue static-universe readings.
The common thread is not a dispute about the measurement — the redshift–distance correlation is accepted here — but about whether the constant of proportionality describes motion or describes propagation.