Is the Hubble Constant Scale-Dependent?

Abstract

An exact determination of the Hubble constant remains one of key problems in cosmology for almost a century. However, its modern values derived by various methods still disagree from each other by almost 10%; the greater values being obtained by measurements at the relatively small distances (e.g., by Cepheid stars as the standard candles), while the smaller values being characteristic of the methods associated with huge spatial scales (e.g., the analysis of the cosmic microwave background fluctuations). A reasonable way to resolve this puzzle is to assume that the Hubble constant is inherently scale-dependent. This idea seems to be particularly attractive in light of the latest observational results on the early-type galaxies, where the dark-matter haloes are almost absent. Therefore, an average contribution of the irregularly-distributed dark matter to the rate of the cosmological expansion should be substantially different at various spatial scales. As follows from the rough estimates, the corresponding variation of the Hubble constant can be 10% and even more, which well explains the spread in its values obtained by the various methods. PACS numbers: 98.80.Es, 95.35.+d, 95.36.+x, 98.62.Gq

On the relation of the lunar recession and the length-of-the-day

“…While these two numbers may be regarded as a puzzling coincidence, the mystery plot thickens with two independent astrometric and radiometric Cassini data (Lainey et al 2020) measurements of the mean recession speed of Titan from Saturn v ≈ 11.3 cm/yr, which when evaluated for the average Titan-Saturn distance D = 1 221 870 km, results in Ḋ/D ≈ 0.9 • 10 −8 cy −1 . The possibility of a scale-dependent Hubble constant has also been raised already by Krizek et al (2015), Dumin (2018), Krizek et al (2021). However, as it is well-known, the observed recession is currently thought to be only produced by the tidal interaction in the Earth-Moon system, which slows down the Earth rotation and thus produces an increase of the length-of-the-day.…”

“…In the above considerations, we have used the Hubble constants at the local and cosmic scales to be the same. However, in principle, it could be conceived that the local Hubble constant might be somewhat different from the one at the global scale (e.g., by 10 − 20%), for more details, the reader is referred to the works by Dumin (2008), Krizek et al (2015), Dumin (2018), Krizek et al (2021). Allowing such freedom in the value of the local Hubble expansion could be utilized to fit the data better.…”

On the Relation of the Lunar Recession and the Length-of-the-Day

“…While these two numbers may be regarded as a puzzling coincidence, the mystery plot thickens with two independent astrometric and radiometric Cassini data (Lainey et al 2020) measurements of the mean recession speed of Titan from Saturn v ≈ 11.3 cm/yr, which when evaluated for the average Titan-Saturn distance D = 1 221 870 km, results in Ḋ/D ≈ 0.9 • 10 −8 cy −1 . The possibility of a scaledependent Hubble constant has also been raised already by Krizek et al (2015); Dumin (2018); Krizek et al (2021). However, as it is well-known, the observed recession is currently thought to be only produced by the tidal interaction in the Earth-Moon system, which slows down the Earth rotation and thus produces an increase of the length-of-the-day.…”

“…The conclusions were that there is some expansion, but the effects were found insignificant, for example Sereno & Jetzer (2007) estimate an expansion of the Earth-Sun distance with a rate of 10 −21 m/yr. There is a noticeable exception with Dumin (2016Dumin ( , 2020, who applies a new metric inspired from the original Kottler metric (Kottler 1918), which accounts for a central mass (cf. Schwarzschild metric) and the Λ-term (cf.…”

“…The relation between the lunar recession and the change of the LOD depends on a number of effects, astronomical, geophysical, climatic and atmospheric. Regarding the possibility of some additional contribution from cosmological expansion, Dumin (2016) points out that "It is quite surprising that many theorists believe that the possibility of local cosmological influences is strictly prohibited just by the available observational data, while a lot of observers believe that there are irrefutable theoretical proofs that Hubble-Lemaître expansion is absent at small scales." On both sides, the situation is still rich of uncertainties and this is what we try to study here.…”