@Soretna , here's the alternative being proposed..though MOND is still a work in progress :-
MOND AS AN EFFECTIVE THEORY
But, on the more fundamental side, the above proximity may hint at a deep connection between cosmology and local dynamics in systems that are very small on cosmological scales. Either cosmology somehow enters and affects local laws of physics, such as the law of inertia or the law of gravity, or a common agent affects both cosmology and local physics so as to leave on them the same imprint. This would mean that MOND-and perhaps more cherished notions, such as inertia-is a derived concept, or an effective theory as we would say nowadays. An observed relation between seemingly unrelated constants appearing in a theory (in our case, a 0, the speed of light, and the radius of the horizon) may indicate that it is only an approximation of a theory at a deeper stratum, in which some of the constants do not really have any special role. A parable will help clarify the point: In experiments and observations confined to the vicinity of the earth surface, there appears a constant: the free-fall acceleration, g. If, for some reason, we were restricted to such an ant world (for example because the earth is ever clothed in a thick layer of clouds) unaware of planetary motions, universal gravity, etc., we would have looked on g as a true constant of nature. We would also notice a mysterious relation between this acceleration and two other important constants: the escape speed c e (objects thrown with a higher velocity never return) and the radius of the earth R 
. This relation: g = c e2 / 2R , is practically the same as that between a 0, the speed of light, and the Hubble radius, in MOND. But, we do see beyond the earth's surface, and we do know about universal gravity, which tells us that the "constants" g and c e actually derive from the mass and radius of the earth (hence the relation between the three). They are useful parameters when describing near-earth-surface phenomena, but quite useless in most other circumstances. In a similar vein, a 0 might turn out to be a derived constant, perhaps variable on cosmic time scales, perhaps even of no significance beyond the non-relativistic regime, where MOND has been applied so far. Its connection with the speed of light and the radius of the universe will, hopefully, follow naturally in the underlying theory that still eludes us.
Many instances of such effective theories are known. Even General Relativity is now thought to be an effective, low-energy approximation of a "higher" theory (e.g. a string-inspired theory); an idea that has been anticipated by Sakharov's "induced gravity" idea.
https://www.semanticscholar.org/paper/SAKHAROV'S-INDUCED-GRAVITY%3A-A-MODERN-PERSPECTIVE-Visser/f4bb5b0b9265a4a71d18a07cf42b6b3eac34481b
The rise and fall of cosmological hypotheses
MILGROMIAN DYNAMICS
NOVEMBER 20, 2020 / MORITZ HASLBAUER / 2 COMMENTS
(by Moritz Haslbauer, 20th Nov. 2020, 18:00)
A directly-related presentation by Moritz Haslbauer and Indranil Banik on the KBC-void and the Hubble tension in the ÎCDM model and Milgromian dynamics can found on the Youtube Channel âCosmology Talksâ by Shaun Hotchkiss: Maybe Milgromian gravity solves the Hubble tension!? â The KBC void & νHDM model (Haslbauer & Banik)
The Universe evolves through expansion and gravitation of matter, which leads to some regions having more galaxies and others having fewer. These variations directly reflect the way in which gravity has created structures out of initial density fluctuations over the last 14 billion years. Thus, the observed spatial arrangement of galaxies on scales ranging from 100 kpc to a Gpc is a very powerful test of different cosmological models and gravitational theories.
In our paper âThe KBC void and Hubble tension contradict ÎCDM on a Gpc scale â Milgromian dynamics as a possible solutionâ (Moritz Haslbauer, Indranil Banik, Pavel Kroupa 2020), we tested if the observed spatial arrangement of galaxies on a Gpc scale can be explained by the standard model (Lambda-Cold Dark Matter, ÎCDM) of cosmology. We also tested if a Milgromian dynamics (MOND) model works.
Several surveys covering the entire electromagnetic spectrum (ranging from radio to X-rays) made an exciting discovery: we are in a Gpc-sized region of the Universe containing far fewer galaxies than ought to be in this volume if ÎCDM were correct.
For example, Karachentsev 2012 found a significant lack of galaxies within a sphere of radius 50 Mpc centered on the Local Group. He reported that the average mass density is a factor of 3-4 lower than predicted by the standard model of cosmology. In 2013, Keenan, Barger, and Cowie discovered that the local Universe is underdense on a much larger scale by counting galaxies at near-infrared wavelengths. They found evidence for an incredibly huge void (hereafter the KBC void) with a density about two times lower than the cosmic mean density and with a radius of about one billion light years (or 300 Mpc). This is about 2% of the distance to the observable Universeâs horizon (about 14 Gpc). The KBC void is shown in Figure 1 below.
Figure 1. The KBC void: the actual density of normal matter divided by the mean cosmological density is plotted in dependence of the distance from the position of the Sun (which is in the Local Group of galaxies). The grey area indicates the density fluctuations allowed by the ÎCDM model. Taken from fig. 1 in Kroupa (2015).
The results by KBC are striking because the ÎCDM model predicts root-mean-square (rms) density fluctuations of only 0.032, while the observed value is 0.46 with an uncertainty of 0.06. This drew our attention, so we decided to investigate the local matter field further in both the ÎCDM and MOND paradigms.
First, we started to quantify the likelihood of a KBC-like void in the ÎCDM model. Using one of the largest cosmological ÎCDM simulations (called MXXL), we rigorously confirmed our suspicion: Einsteinian/Newtonian gravity is simply too weak to form such deep and extended underdensities like the KBC void. Our calculations showed that the KBC void alone falsifies ÎCDM with a significance much higher than the typical threshold used to claim a discovery, e.g. with the famous Higgs boson. Consequently, the KBC void is totally inconsistent with the current standard model, implying that the observed Universe is much more structured and organized than predicted by ÎCDM. A similar conclusion was reached by Peebles & Nusser 2010 on much smaller scales by studying the galaxy distribution within the Local Volume, a sphere with 8 Mpc radius centred on the Local Group. And the whole Local Group is also âgrievouslyâ structured (Pawlowski, Kroupa, Jerjen 2013), showing a âfrightening symmetryâ as called by Pavel Kroupa.
The implications of the observed local density contrast on a Gpc scale are far-reaching, because so far it was widely understood that the ÎCDM paradigm provides a very successful description on this scale. Given the many failures of ÎCDM on galaxy scales (e.g. Kormendy et al. 2010 , Kroupa et al. 2010, Kroupa 2012, Kroupa 2015, Pawlowski et al. 2015), the ÎCDM model now faces significant problems across all astronomical scales. A compilation of failures, many of which have reached the 5sigma confidence threshold of ÎCDM failure, can be found in the previous contribution to the Dark Matter Crisis.
The observed spatial arrangement of galaxies on scales ranging from 100 kpc (the satellite planes) to 300 Mpc (our work) strongly suggests that structure formation is much more efficient than possible by Newtonâs gravitational law, implying a long-range enhancement to gravity over that allowed by Newtonian gravity. This is in fact not surprising, given that Newton and Einstein both only had Solar System data at their disposal to formulate their theories; gravitation is after all, the least understood of the fundamental interactions. Consequently, we next studied the formation of structures in Milgromian dynamics, which was developed by Israeli physicist Mordehai Milgrom in 1983 (Milgrom 1983). MOND is a corrected version of Newtonian gravitation taking into account galaxy data which were non-existing for Newton and for Einstein. MOND successfully predicted many galaxy scaling relations, but has rarely been applied to cosmological scales.
We extrapolated the MOND model from galactic to a Gpc scale by applying the Angus 2009 cosmological MOND model. This Angus cosmological model has a standard expansion history, primordial abundances of light elements, and fluctuations in the cosmic microwave background (CMB), mainly because both the ÎCDM and MOND cosmology have the same mass-energy budget. However, instead of cold dark matter particles, the MOND model assumes fast-moving collisionless matter, most plausibly in the form of 11eV/c^2 sterile neutrinos. The existence of sterile neutrinos is motivated by particle physics, since they could explain why the ordinary neutrinos have mass. The low mass of hypothetical sterile neutrinos means they would clump on large scales (e.g. galaxy clusters), but not in galaxies, thus leaving their rotation curves unaffected. The following is in fact a most important point to emphasize: The Angus cosmological model needs extra fast moving matter which comes from standard particle physics (but still needs to be verified experimentally). This is very different to the ÎCDM model which needs dark matter particles that account for the observed rotation curves in disk galaxies but which are not motivated to exist by the standard model of particle physics.
The enhanced growth of structure in Milgromian gravitation generates much larger and deeper voids than in Einsteinian/Newtonian gravity. This leads to the formation of KBC-like voids as shown in our paper. Such an extended and deep underdensity causes an interesting effect: parts of the Universe beyond the void with more galaxies pull galaxies in the void outwards. This changes the motions of galaxies, making the local Universe appear to expand faster than it actually is. The situation is illustrated in Figure 2.
Figure 2: Illustration of the Universeâs large scale structure. The darker regions are voids, and the bright dots represent galaxies. The yellow star represents the position of our Sun. Note that the Sun is not at the centre of the KBC void. The arrows show how gravity from surrounding denser regions pulls outwards on galaxies in a void. If we were living in such a void, the Universe would appear to expand faster locally than it does on average. This could explain the Hubble tension. Interestingly, a large local void is evident in the entire electromagnetic spectrum. Credit: Technology Review
Indeed, local observations of how quickly the Universe is expanding exceed the prediction of ÎCDM by about 9%. This so-called Hubble tension is one of the greatest mysteries in contemporary cosmology. In our paper we showed that the unexpectedly high locally measured Hubble constant is just a logical consequence of enhanced structure formation in MOND, and us residing within a particularly deep and large void. This Hubble bubble scenario is however not consistent with ÎCDM because it does not allow for a sufficiently extreme void (Figure 3).
Figure 3: In our paper we showed that that the KBC void cannot form out of the initial conditions of the CMB at redshift z = 1100 if Einsteinian/Newtonian gravity is assumed. Adding the speculative cold dark matter does not help. Therefore, the Hubble tension cannot be explained by the KBC void in the context of the ÎCDM paradigm. Consequently, we aimed to study the formation of structures in Milgromian dynamics. The long-range enhancement to gravity in MOND allows the formation of KBC-like voids, which simultaneously explains the high locally measured Hubble constant.
Thus, the current hot debate among astronomers about the expansion of the Universe being different close to us than far away only exists because astronomers are using the wrong model. A universe which does not have exotic cold dark matter particles but runs on Milgromian gravitation ends up looking just like the real Universe, at least with the tests done thus far.
There is now a real prospect of obtaining a MOND theory of cosmology that explains the data from dwarf galaxies up to the largest structures in the Universe much better than the ÎCDM framework. Consequently, the here described cosmological MOND framework could be a way out of the current crisis in cosmology.
Given my affiliation with Charles University, I have been travelling to Prague and beyond frequently and now the CORONA Pandemic has stopped this flying about the planet â I have already written about the first wave and my getting marooned on a beautiful island next to the Strand. Being this time stranded in Bonn without a Strand during the second wave, I have a little more time on my hands I guess. So here we are, back to the Crisis.
In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.
Regards
