E. Conover in the paper “Debate over the universe’s expansion rate may unravel physics. Is it a crisis?” outlined the following situation with the measurements of an expansion rate of the universe [2]:

· Scientists with the Planck experiment have estimated that the universe is expanding at a rate of 67.4km/s Mpc with an experimental error of 0.5km/s Mpc;

· But supernova measurements have settled on a larger expansion rate of 74.0km/s Mpc,with an error of 1.4km/s Mpc. That leaves an inexplicable gap between the two estimates. Now “the community has started to take this [problem]extremely seriously,”says cosmologist Daniel Scolnic of Duke University,who works on the supernova project led by Riess,called SH0ES;

· It is unlikely that an experimental error in the Planck measurement could explain the discrepancy. That prospect is “not a possible route out of our current crisis,”said cosmologist Lloyd Knox of the University of California,Davis;

· So,worries have centered on the possibility that the supernova measurements contain unaccounted for systematic errors—biases that push the SH0ES estimate to larger value.

L. Verde, T. Treu, and A. G. Riess gave a brief summary of the “Workshop at Kavli Institute for Theoretical Physics, July 2019” [3].

Table 1 summarizes the results of measurements of the Hubble constant H₀ in 2019-2021 [4]. Observe that the values of H₀ vary significantly depending on Methodology. The disagreement in the values of H₀ obtained by the various teams far exceeds the standard uncertainties provided with the values. The average values of H₀ vary from 67.4 to 76.8 km∙s⁻¹∙Mpc⁻¹. This discrepancy is called the Hubble tension [5]. A. Mann gave a summary of the situation with the measurements of H₀ in “One Number Shows Something Is Fundamentally Wrong with Our Conception of the Universe” paper [6]. It is not clear whether the discrepancy in the observations is due to systematics, or indeed constitutes a major problem for the Standard model.

W. L. Freedman in the paper “New analysis by UChicago astronomer finds agreement with standard model in ongoing Hubble tension” outlined the following situation with the measurements of an expansion rate of the universe [7]:

· Our universe is expanding, but our two main ways to measure how fast this expansion is happening have resulted in different answers. For the past decade, astrophysicists have been gradually dividing into two camps: one that believes that the difference is significant, and another that thinks it could be due to errors in measurement;

· One way to measure the Hubble constant is by looking at very faint light left over from the Big Bang, called the cosmic microwave background. Scientists can feed these observations into their ‘standard model’ of the early universe and run it forward in time to predict what the Hubble constant should be today; they get an answer of 67.4 kilometers per second per megaparsec;

· The other method is to look at stars and galaxies in the nearby universe and measure their distances and how fast they are moving away from us. Freedman has been a leading expert on this method for many decades; in 2001, her team made one of the landmark measurements using the Hubble Space Telescope to image stars called Cepheids. The value they found was 72;

· The value of the Hubble constant Freedman’s team gets from the red giants is 69.8 km/s/Mpc—virtually the same as the value derived from the cosmic microwave background experiment.

In the article “Measurements of the Hubble Constant: Tensions in Perspective,” W. L. Freedman provides an excellent review of the Hubble Constant measurements [8]:

· As apparent fissures in the standard model have been emerging, there are also indications that there may be cracks that need attention in the local distance scale as well. For example, the Tip of the Red Giant Branch (TRGB) method and the Cepheid distance scale result in differing values of H 0 = 69.6 ± 1.9   km / sec / Mpc (Freedman, et al. 2019, 2020) for the TRGB and 73.2 ± 1.3 (Riess et al. 2021) for the Cepheids;

· In contrast, (early-time) estimates of H₀ based on measurements of fluctuations in the temperature and polarization of the cosmic microwave background (CMB) from Planck and ACT+WMAP (Planck Collaboration et al. 2020; Aiola et al. 2020) consistently yield lower values of H 0 = 67.4 ± 0.5 and 67.6 ± 1.1   km ⋅ s − 1 ⋅ Mpc − 1 , respectively, both adopting the current standard ΛCDM model;

· High values of H₀ were initially obtained from time-delay measurements of strong gravitational lensing (Suyu et al. 2017; Wong et al. 2020), with H 0 = 73 − 1.8 + 1.7   km ⋅ s − 1 ⋅ Mpc − 1 , apparently consistent with the Cepheid measurements. However, recent detailed consideration of the assumptions in the modeling of the lens mass distribution (Birrer et al. 2020; Birrer & Treu 2020) leads to a much lower value of the Hubble constant, as well as a significantly larger value of the uncertainty H 0 = 67.4 − 3.2 + 4.1   km ⋅ s − 1 ⋅ Mpc − 1 , currently consistent with the CMB and TRGB measurements;

· This TRGB calibration was updated slightly in (Freedman et al, 2020), yielding a value of H 0 = 69.6 ± 0.8 ( stat ) ± 1.7 ( sys ) km ⋅ s − 1 ⋅ Mpc − 1 . To date, the TRGB is the only method with comparable numbers of galaxies in its calibration relative to Cepheids; the H₀ calibration of Riess et al. (2016, 2019), is based on the Cepheid distances to 19 galaxies. Ten of the galaxies in the (Freedman et al, 2019) and (Freedman et al, 2020) TRGB sample also have independent Cepheid distances, an order of magnitude greater number than for Miras (Huang et al. 2020) or the maser technique (Pesce et al. 2020), in both cases for which only a single galaxy is available for comparison with Cepheids;

· The updated TRGB calibration applied to a distant sample of Type Ia supernovae from the Carnegie Supernova Project results in a value of the Hubble constant of H 0 = 69.8 ± 0.6 ( stat ) ± 1.6 ( sys ) km ⋅ s − 1 ⋅ Mpc − 1 . No statistically significant difference is found between the value of H₀ based on the TRGB and that determined from measurements of the cosmic microwave background.

Laniakea Supercluster (LSC) is a galaxy supercluster that is home to Milky Way (MW) and approximately 100,000 other nearby galaxies (see Figure 1). It is known as one of the largest superclusters with estimated binding mass 10¹⁷M_ʘ [9]. The neighboring superclusters to LSC are the Shapley Supercluster, Hercules Supercluster, Coma Supercluster, and Perseus-Pisces Supercluster. Distance from the Earth to the Centre of LSC is 250 Mly, Redshift—0.0708 (center).

The mass-to-light ratio of the Virgo Supercluster is about three hundred times larger than that of the Solar ratio. Similar ratios are obtained for other superclusters [10]. In 1933, F. Zwicky investigated the velocity dispersion of Coma cluster and found a surprisingly high mass-to-light ratio (~500). He concluded: “If this would be confirmed, we would get the surprising result that dark matter

is present in much greater amount than luminous matter” [11]. These ratios are one of the main arguments in favor of presence of substantial amounts of Dark Matter in the World.

We emphasize that about 100,000 nearby galaxies are moving around Centre of Laniakea Supercluster. They belong to LSC. All these galaxies did not start their movement from the “Initial Singularity”. The neighboring superclusters have the same structure (see Figure 2 and Figure 3). It means that the World is, in fact, a Patchwork Quilt of different Luminous Superclusters (≳10³) [12].

According to R. B. Tully, et al., “Galaxies congregate in clusters and along filaments, and are missing from large regions referred to as voids. These structures are seen in maps derived from spectroscopic surveys that reveal networks

of structure that are interconnected with no clear boundaries” [13] .

P. Wang, et al. made a great discovery: “Most cosmological structures in the universe spin. Although structures in the universe form on a wide variety of scales from small dwarf galaxies to large super clusters, the generation of angular momentum across these scales is poorly understood. We have investigated the possibility that filaments of galaxies—cylindrical tendrils of matter hundreds of millions of light-years across, are themselves spinning. By stacking thousands of filaments together and examining the velocity of galaxies perpendicular to the filament’s axis (via their red and blue shift), we have found that these objects too display motion consistent with rotation making them the largest objects known to have angular momentum. These results signify that angular momentum can be generated on unprecedented scales” [14].

A. Lopez reported about the discovery of “a giant, almost symmetrical arc of galaxies—the Giant Arc—spanning 3.3 billion light years at a distance of more than 9.2 billion light years away that is difficult to explain in current models of the Universe. This new discovery of the Giant Arc adds to an accumulating set of (cautious) challenges to the Cosmological Principle. The growing number of large-scale structures over the size limit of what is considered theoretically viable is becoming harder to ignore. Can the standard model of cosmology account for these huge structures in the Universe as just rare flukes or is there more to it than that?” [15] .

WUM. These latest observations of the World can be explained in frames of the developed WUM only [1]:

· “Galaxies do not congregate in clusters and along filaments.” On the contrary, Cosmic Web that is “networks of structure that are interconnected with no clear boundaries” is the result of the Explosive Volcanic Rotational Fission of Dark Matter (DM) Cores of neighboring Superclusters;

· “Generation of angular momentum across these scales” provide DM Cores of Superclusters through the Explosive Volcanic Rotational Fission;

· “Spinning cylindrical tendrils of matter hundreds of millions of light-years across” are the result of spiral jets of galaxies generated by DM Cores of Superclusters with internal rotation;

· The Giant Arc is the result of the intersection of the Galaxies’ jets generated by the neighboring DM Cores of Superclusters;

· 13.77 Gyr ago, when the Laniakea Supercluster emerged, the estimated number of DM Supercluster Cores in the World was around ~10³ [12]. It is unlikely that all of them gave birth to Luminous Superclusters at the same cosmological time being far away from each other. The 3D Finite Boundless World presents a Patchwork Quilt of different Luminous Superclusters, which emerged at different Cosmological times.

The experimental observations of galaxies in the universe show that most of them are disk galaxies [16]. It is well-known, that while observing spiral galaxies, a side spinning toward us has a slight blueshift relative to the center of the galaxy whereas the side spinning away from us has a slight redshift. Therefore, there is a meaning of a redshift of a Center of galaxy only. The redshift of the Centre of LSC is 0.0708. But it does not mean that LSC is moving away from MW. On the contrary, MW is moving away from the Centre of LSC. In LSC, some galaxies are moving toward MW, and the other are moving away (see Figure 1). Then redshift depends on the position and movement of a particular galaxy in LSC against MW. More complicated situation with redshift is when galaxies belong to neighboring superclusters, which emerged at different cosmological times.

According to WUM, the value of the Hubble parameter H depends on the cosmological time: H = τ − 1 . It means that a value of H should be measured based on Cosmic Microwave Background (CMB) radiation only. Figure 4 illustrates recent H₀ determinations using only CMB data.

The calculated value of Hubble constant in 2013 [18]: H 0 = 68.733   km / s ⋅ Mpc is in excellent agreement with the most recent measured value in 2021: H 0 = 68.7 ± 1.3   km / s ⋅ Mpc using only CMB data [17].

In frames of WUM, the Hubble tension can be explained the following way:

· All measurements of Hubble constant are model-dependent;

· Statistics of these measurements is not sufficient to yield reliable conclusions;

· Hubble’s law in Standard Cosmology is valid for the Big Bang Model (BBM) only when all galaxies start their movement from a single point named “Initial Singularity” that is not the case in WUM;

· There are observations of Galaxies, which belong to different Superclusters;

· The value of H depends on the cosmological time H = τ − 1 and is higher for the earlier Epoch of the World. It means that the value of H should be measured for each Galaxy separately depending on a distance to it and corresponding cosmological time. We must not calculate average values of H depending on Methodology as it is done in Table 1;

· The value of H should be measured based on Cosmic Microwave Background Radiation only.

This explanation is in good agreement with the experimental results provided by W. L. Freedman who belongs to the camp that believes that the difference could be due to errors in measurement. I belong to the camp that believes that the difference is significant.

The main differences between BBM and WUM are:

· Mainstream scientists, following BBM, measure the values of the Hubble constant based on various characteristics of Macroobjects, the distribution of which in the World is spatially Inhomogeneous and Anisotropic and temporally Non-simultaneous;

· WUM suggests that the value of the Hubble constant should be measured based on Cosmic Microwave Background Radiation only, which depends on the characteristics of the Medium of the World. The Medium is Homogeneous and Isotropic. Its parameters do not practically depend on Macroobjects, which can create some fluctuations in the Medium.

Special thanks to my son Ilya Netchitailo who helped me refine the Model and improve its understanding.

The author declares no conflicts of interest regarding the publication of this paper.

Netchitailo, V.S. (2022) Hubble Tension. Journal of High Energy Physics, Gravitation and Cosmology, 8, 392-401. https://doi.org/10.4236/jhepgc.2022.82030