Winnie-the-Pooh came to a village far away from Hundred Acre Wood in which, as he had heard, stood a great jar of the very best honey to be found anywhere. Bears and honey, oh boy. The jar of honey was very famous. Everyone far and wide was saying — because they had had it heard being confirmed by everyone all the time — that this honey is especially very special because it is invisible. And so many other inhabitants of the woods and meadows came to look at The Jar, even from very far places no-one had ever heard of. Many of the rich visitors even hoped to be able to get a taste of this famous invisible honey. The jar was famously called “The Jar Full of Invisible Hunny”. Winnie-the-Pooh wanted to later take his friends, Christopher Robin and Piglet, to also see this Jar Full of Invisible Hunny. Maybe Christopher could buy some of the famous invisible hunny for Winnie-the-Pooh? But it must be very very expensive, so Winnie-the-Pooh thought he should first have a look.
Winnie-the-Pooh (copyright A.A. Milne and E.H. Shepard; credit: Winnie The Pooh 2011 51st Disney’s classic).
Winnie-The-Pooh was very impressed by the great size of The Jar of Invisible Hunny and really wanted to get a taste of this very best honey. But no-one was allowed to look into the The Jar, and when someone did manage to sneak a glance in, they confirmed that it is truly The Jar of Invisible Hunny. Being a clever bear albeit with a very slow mind, Winnie-The-Pooh thought, after some time of looking at The Jar Full of Invisible Hunny, that he might learn a little more about this invisible hunny by knocking on the side of The Jar. He went up to The Jar, embraced it to show his gratitude of being near it, and quickly, so no-one noticed, knocked. The sound he received made him raise his eyebrows – the clanking he heard in return sounded as if The Jar was empty!
Somewhat disconcerted and very thoughtful, Winnie-the-Pooh sat back and looked at The Jar supposedly Full of Invisible Hunny. After some time (the Sun had moved from the left to the right) of very intense thinking, a thought slowly and unstoppably formulated in the bears mind: might it be that The Jar Full of Invisible Hunny is (supposedly) full of “Invisible Hunny” because there is no hunny inside The Jar? Very bothered with his new very Uncomfortable Thought, Winnie-the-Pooh got up and walked around the village and spoke to anyone who would be willing to listen to him. And every time Winnie-the-Pooh explained the Uncomfortable Thought, the listener stopped listening, calling the bear a very impolite bear who should stop having such Uncomfortable Thoughts, behave as everyone else and just accept that The Jar Full of Invisible Hunny is FULL of Invisible Hunny. This has been confirmed by many who have had it confirmed with utmost certainty by others, and there is no question about The Jar Full of Invisible Hunny being FULL of Invisible Hunny. EVERYONE knows this!
No-one believed Winnie-the-Pooh. Some even suggested that the bear be removed from the village and put into a hole as the bear’s Uncomfortable Thought might spread to those dimm wits with lesser minds. After all, the village wants everyone to come because the visitors bring affluence. Winnie-the-Pooh became very unhappy, and sat down again in moonlight as the Moon started to climb up its ladder. By the time Winnie-the-Pooh had to look straight up to see the Moon, a plan had formulated in the bear’s mind:
"If I am not allowed to taste the invisible hunny, I can at least see if I can remove the Uncomfortable Thought from my thoughts and become like everyone else, by dropping a small stone into The Jar Full of Invisible Hunny. If the stone falls through to the bottom or The Jar ever more rapidly, as if it were falling outside of The Jar Full of Invisible Hunny, then the Jar Full of Invisible Hunny is a jar without hunny in it and my Uncomfortable Thought would become a Bother. But if the stone falls into The Jar Full of Invisible Hunny and stops for a while before sinking down slowly to the bottom of The Jar Full of Invisible Hunny then The Jar Full of Invisible Hunny is indeed full of invisible hunny."
The Winnie-the-Pooh Test
Winnie-the-Pooh became very proud of himself because he had managed to have such a great idea for such a complicated test, but he became very worried about the possible outcome of this ultimate experiment.
So when everyone was sleeping and the Moon had climbed down on the other side, Winnie-the-Pooh collected a little stone, cleaned it in a nearby stream, borrowed the same ladder and climbed up the Jar Full of Invisible Hunny. Looking around to make sure no-one saw his very secret and surely forbidden experiment, Winnie-the-Pooh dropped the little stone into the jar. It fell right through landing on the jar’s bottom with a clanking sound. The Jar Full of Invisible Hunny was completely empty.
Winnie-the-Pooh returned the ladder to where he had gotten it from so as to have no-one raise suspicion and sat down. His tummy was by now rumbling away and also increasingly unhappy, because it was very hungry. So Winnie-the-Pooh first needed to get his tummy, his best pal, happy, and he decided to look for a non-empty pot of honey, or some condensed milk, or something else that would make tummy happy.
Winnie-the-Pooh left the village with The Jar Full of Invisible Hunny which he now knew was an empty jar. He reasoned with himself: “oh bother, there’s nothing I can do about the large jar empty of hunny. No-one listens to me and no-one cares about knowing the truth, I do not want to end up in a hole and my tummy will have none of it anymore”.
In The Dark Matter Crisis by Elena Asencio, Moritz Haslbauer and Pavel Kroupa. A listing of contents of all contributions is available here.
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The Cosmology Group at the Astronomy Lab of the Aristotle University of Thessaloniki is organising a conference on the above problem. The organisers are PhD student Asvesta Kerkyra with professor Leandros Perivolaropoulos and professor Christos Tsagas.
The conference will take place from June 3rd until June 6th on site in Aristotle University. Further information can be found at this link.
In The Dark Matter Crisis by Elena Asencio, Moritz Haslbauer and Pavel Kroupa. A listing of contents of all contributions is available here.
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Readers may be interested in two on-line meetings that are coming up:
1. Challenges of Modern Cosmology 2024 (CMC2024): January 18th
CMC2024 is an online discussion panel intended for listening, sharing and learning about challenges of modern cosmology and alternative theories. It will take place on the 18th of January 2024 from 12:00 to 17:00 (CET) and it will be publicly streamed on youtube. The panel will be divided in three sessions: current problems of modern cosmology, modified cosmology and gravity theories, and standard cosmological and gravitational tests. Each of these sessions will include from two to three 10 minutes talks followed by a 20 minutes discussion on the corresponding topic of the talk.
In order to join the discussion panel, registration is still possible until the 10th of January. The discussion can also be followed online without registration by searching for “CMC2024” on youtube or directly through. Before lunch break:
After lunch break:
Participation in social media to share comments or questions is also possible by using, for example, the X-hashtag #cosmos24.
2. Challenging the standard cosmological model: April 15th-16th
Scientific discussion meeting organised by Professor James Binney FRS, Dr Roya Mohayaee, Professor John Peacock FRS and Professor Subir Sarkar. See this link for the details and the registration for researchers in relevant fields.
In The Dark Matter Crisis by Elena Asencio, Moritz Haslbauer and Pavel Kroupa. A listing of contents of all contributions is available here.
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It seems that experts have a conference once a month somewhere on the globe to discuss why the local Universe seems to be expanding faster than the global Universe. Local expansion is obtained by using standard candles, the type Ia supernovae that explode in galaxies, by associating their distances to their recessional speeds. Global expansion is obtained by fitting the standard cosmological model to the cosmic microwave background (CMB) properties. This Hubble Tension is keeping hundreds if not thousands of astronomers and physicists busy in their jet-setting around the world to meet at repeating conferences at which the latest ideas on exotically complex, time or space-dependent dark energy descriptions are announced as possible solutions to the Hubble Tension. It keeps many bright people busy and some at a very elevated state of fame: “We have discovered a major new mystery of the Universe and only the very brightest of minds will be able to solve it.” Such minds can only be found in Ivy League Universities. I have been at a few such conferences (DMC Nr.77). I noted that it is not a problem for this group of scientists that the standard Einstein/Newtonian–inflation–plus–dark-matter–plus–dark-energy (the LCDM) model (I include here warm and fuzzy dark matter versions as these are extremely similar to the cold-dark matter version) does not conserve energy.
It is simply accepted that this model universe (which nearly everyone thinks is the real Universe) accelerates its expansion driven by a dark energy that no one understands and that creates more space and energy ever faster without an end.
Why is dark energy even needed? Well, assuming Einstein/Newtonian gravitation plus inflation plus dark matter leads to a model universe that would today globally expand too slowly. The only way to fix this overall expansion problem is to include an additional hypothetical process which pulls the model universe apart, and this is dark energy. The draw back of this fix is the above infinite-energy problem.
Interesting in this is also the systematic ignoring of the obvious solution to the Hubble Tension problem: the simple fact that our Local Group of Galaxies (about 10 million light years across) is located in a cosmological void of matter which is some 3 billion light years across. This region contains fewer galaxies than other regions and is observed in all surveys that have been done to date — see Figure 1.
Figure 1: The local void: the y-axis shows, essentially, the ratio between the observed number of galaxies divided by the expected global-mean-value in the LCDM model and the x-axis shows the distance from our Local Group (one pc is about 3.3 light years and h70 is about one). The inset indicates the literature where the data come from. The observational data tell us that at distances further than about 1200 light years (400Mpc) an about constant average space density of galaxies is reached, but that at smaller distances we are seeing a significantly smaller number of galaxies per unit volume. This is the local void (also referred to as the KBC void after Keenan-Barger-Cowie, or the local hole already described by Tom Shanks and his collaborators since 2003. Note that the underdensity is much deeper than allowed by the LCDM model (the shaded region). This figure is from Kroupa (2015).
“Thus, the present 2MASS data suggest the presence of a potentially huge contiguous void stretching from south to north. Not only would this delineate further the limits for the cosmological principle but it would also show the possible presence of significant power on scales of >~300 h-1 Mpc in the galaxy power spectrum.”
In the above Mazurenko et al. (2023) work, a cosmological model was employed to calculate the growth of structures. The model is (yes, obviously) MOND-based and works without cold, warm or fuzzy dark matter (which by now everyone should know does not exist). This cosmological model leads to the growth, as cosmological time progresses, of density differences between different regions. It turns out that the type of under-density, such as is evident in Figure 1, arises naturally. The first-ever hydrodynamical simulations of structure formation in this “nuHDM model” was published by us in Bonn (Wittenburg et al. 2023).
These under-densities (and corresponding overdensities) develop in this MOND-cosmological model because the effective gravitational force is stronger allowing the tiny initial fluctuations observed in the CMB to grow to more pronounced structures than in the LCDM model. These same fluctuations produce a completely uniform and smooth model universe in LCDM when viewed on scales larger than some 600 million light years, while leading to a much more clumpy and irregular model universe in a MOND-based cosmological model on even larger scales. In two previous publications (2021 and 2023) our study in Bonn led by PhD student Elena Asencio and Indranil Banik have also shown that the very massive galaxy cluster El Gordo, observed to already exist at the redshift of 0.87, arises naturally in such a model. In the LCDM model this is quite impossible (the Bullet Cluster, by the way, is also a challenge for the LCDM model but is easy in MOND-cosmology, as explained by Elena in her publications). See DMC Nr. 84.
We thus have the following physical situation: The (correct — in the sense of not having cold or warm of fuzzy dark matter but a realistic gravitational law) MOND-cosmology grows large regions of matter underdensities (as well as major overdensities and massive galaxy clusters). Being in an underdensity, the observer finds that the galaxies in it are falling towards the sides of the underdensity, just like apples fall to the ground on Earth (Isaac Newton would probably have appreciated this — see Figure 2).
Figure 2: The image shows the schematic distribution of matter in space – (blue; the yellow dots represent individual galaxies). The Milky Way (green) lies in an area with little matter. The galaxies in the bubble move in the direction of the higher matter densities (red arrows – imagine these are apples). The universe therefore appears to be expanding faster inside the bubble.
This is the reason why the observer thinks the local Universe is expanding at a slightly faster rate than the global Universe. Given that the underdensity is observed to be there through a lack of galaxies (Figure 1), this solution to the “Hubble Tension” is straight-forward – it is in fact so trivial that the leading minds in cosmology (the elite) appear to be challenged in grasping it — it seems that the whole research community, as shepherded by the brilliant minds in Ivy League institutions, appears to be acting as if it were the Catholic Church some 400 years ago concerning MOND: MOND is a sacrilegious topic not to be talked about by those that want to matter, and any way, every one knows it is wrong and also not a theory (well, the wide-binary-star test of MOND lately causes some heated debate among the few people who have the skills to make calculations in MOND and will be addressed here in the near future).
In any case, given this explanation of the Hubble Tension in a MOND-based cosmological model, our model as published in Haslbauer et al. (2020)makes a prediction! The prediction is: in the model (which accounts for the underdensity — Figure 1 — and the Hubble Tension as published by Haslbauer et al. 2020, and which does not take into account any measurements of bulk velocities AT ALL), galaxies must be moving faster away from us the further they are, after subtracting the Hubble expansion. That is, the model predicts (before the measrurement) that the bulk flow speed of galaxies increases with increasing distance.
And the sensational thing about all of this is: this prediction has now been confirmed! Watkins et al. (2023) measure “the bulk flow in a volume of radii 150-200 h-1 Mpc using the minimum variance method with data from the CosmicFlows-4 (CF4) catalogue.” Figure 3 shows the measured bulk flow: For example, galaxies observed at a distance of 200/h Mpc (about 600 million light years) show a bulk velocity of about 420 km/s (after correcting for the Hubble expansion). The MOND-based cosmological model gives the same velocity if the Local Group (the green dot in Figure 2) is approximately 380 million light years (116 Mpc) away from the centre of the void and is moving with a velocity of about 220 km/s relative to the local bulk flow such that the Local Group moves with a total of approximately 627 km/s relative to the CMB.
Figure 3: The bulk flow of galaxies (the average speed of galaxies in a sphere, y-axis) is plotted versus the distance from the observer on the x-axis. The data from Watkins et al. (2023) are shown as solid black dots. The MOND-based cosmological model is shown as the dotted line assuming the local void has a Gaussian density profile, that the Local Group is located 116 Mpc (about 380 million light years) away from the void centre and that the Local Group is moving with 627 km/s relative to the CMB and about 200 km/s slower than the local bulk flow (within some 150 million light years). In other words, the Local Group’s velocity relative to the CMB has been reduced to 627 km/s by small-scale flows in the local region. Thus, the MOND-cosmology-based bulk flow (dotted black line) is in (stunning) agreement with the data in terms of its amplitude and shape, while the LCDM model predicts bulk velocities (solid red line) that are in major disagreement with the observations. Adapted from Mazurenko et al. (2023).
It thus turns out that once we have a better model of the observed Universe, then (i) the local billion light year underdensity, (ii) the Hubble Tension and, simultaneously, (iii) the high observed bulk velocities of the galaxies at distances of a few hundred million light years are automatically and simultaneously understood. This is trivial in the sense that it pops out of the MOND-based calculations, but it is highly non-trivial because no other known model has been able to achieve this.
What of the future? We now have an improved cosmological model, namely the “nuHDM” model. It accounts automatically for open star clusters, galaxies(e.g. Banik & Zhao 2022, Kroupa et al. 2023), the Hubble Tension, bulk flows as well as the significant density contrasts on scales of some billion light years (this text). But open questions remain:
This “nuHDM” MOND-cosmological model is very conservative by assuming a next-to-identical expansion history as the LCDM model. It thus assumes, like the LCDM model, inflation and dark energy, and assumes the CMB is the photosphere of the hot Big Bang. The one major issue therefore is that it is also not energy conserving. To achieve the same expansion history, the mass content of this model universe needs to be dominated by a sterile neutrino background, which effectively is a hot dark matter component that plays no role in galaxies and is less exotic by being related to the physics of the active neutrino. And it solves the missing mass problem in galaxy clusters. As shown in the first-ever hydrodynamical simulations of structure formation in the nuHDM model published by us in Bonn (Wittenburg et al. 2023), it seems to form galaxies too late and by the present time it is populated by too many hugely massive galaxy clusters, posing two additional problems. Further research on this model is needed reaching to much higher resolution. Given these open questions, a new, and bolder model of the Universe is being studied. I call it the Bohemian Model of Cosmology (it is hinted at in Kroupa et al. 2023). Currently we are testing if this model, which is based on radically moving away from the current Belief Canon of the Cosmological Community, stands up to the observational data, ranging from open star clusters to the largest probed cosmological scales.
To summarise: a major step towards an improved understanding of cosmologically relevant observations has been achieved, even though the majority of scientists are still far from accepting this. The real Universe is significantly better matched by a model based on Milgromian dynamics, from the scale of open star clusters to the billion light-year scale. The challenging prospects are to better understand the fundamental physics underlying Milgromian dynamics which appears to be related to the quantum vacuum, and to develop a model universe which conserves energy. It is quite possible that both of these are different aspects of the same solution. Today is truly an exciting time for young scientists to flex their cerebral muscles, perhaps comparable to the 1920s when quantum physics was being discovered to a large extend in Copenhagen and Goettingen.
In The Dark Matter Crisis by Elena Asencio, Moritz Haslbauer and Pavel Kroupa. A listing of contents of all contributions is available here.
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ACT-CL J0102-4915, commonly known as ‘El Gordo‘, is a very peculiar galaxy cluster that stands out due to its extreme properties. This cluster, formed by the collision of two subclusters about seven billion years ago, is considered to be one of the hottest, brightest, and most massive galaxy clusters ever observed. These characteristics have made El Gordo an unsolved mystery in the eyes of the current standard model of cosmology (ΛCDM).
Ever since the first study on El Gordo inferred a mass of 2-3 x 1015 Solar masses for this cluster, several additional studies have attempted to verify and constrain its mass using different observational methods. The most recent studies on this subject (Kim et al. 2021, Caminha et al. 2023, Diego et al. 2023) have determined the mass of El Gordo by measuring the deflection of background light due to the cluster’s gravitational potential, a phenomenon known as gravitational lensing. These studies consistently estimate its mass to be approximately 2 x 1015 Solar masses. Such a high mass at the young cosmological epoch in which El Gordo is observed is very unexpected in the ΛCDM theory of cosmology. This is because, according to this cosmological theory, structure formation relies on smaller structures merging together to form larger structures in a slow process called gravitational accretion. There simply was not enough time to have formed two clusters this massive within striking distance of each other when the universe was only about half its present age.
The other distinctive properties of El Gordo are its X-ray morphology – characterised by its two-tailed shape – and its very high temperature and luminosity. All the hydrodynamical simulations of El Gordo that have been performed so farhave shown that, in order to reproduce these properties, it is required that the two subclusters collided with each other at a very high speed. Explaining how the subclusters could have achieved such a high relative velocity is also a challenge for ΛCDM. This is due to the fact that structures owe their velocities to the expansion of the Universe and to interactions with other structures. Because of dynamical friction, when massive structures interact with less massive structures, they lose energy to these. Therefore, more massive structures are expected to have lower velocities than their escape velocity – but the hydrodynamic simulations indicate this is not the case for El Gordo.
In our recent study (Asencio, Banik & Kroupa 2023), we assessed the probability of observing El Gordo in a ΛCDM universe, assuming a total mass of 2.13 x 1015 Solar masses and a mass ratio of 1.52, as reported by Kim et al. (2021). To do so, we adopted the same method employed in Asencio, Banik & Kroupa (2021). This method consists of using a ΛCDM cosmological simulation to look for analogues of the El Gordo subclusters whose properties could potentially give rise to an object like El Gordo (see the previous post on El Gordo for more detail). This implies that the pair of simulated subclusters must be at a cosmological epoch at least half a billion years prior to that at which El Gordo is observed. They should also be infalling into each other, have a mass ratio smaller or equal to the mass ratio of El Gordo, and have a total mass equal or higher than that of El Gordo. Regarding the minimum infall velocity required for the subclusters to yield a realistic post-collision morphology, we repeated this analysis assuming different values ranging from 1000 km/s to 3000 km/s.
The results of our analysis are summarised in Figure 1. This shows that, in the ΛCDM theory, the El Gordo subclusters would need to have an infall velocity lower than 2300 km/s so that the probability of being observed in their survey region leads to a tension that falls below the 5σ threshold. Events above this threshold correspond to a probability of less than 5.7 x 10-7, which is the widely accepted limit signifying that an event is practically impossible.
Figure 1 showing the probability of observing an El Gordo-like object in a ΛCDM cosmology (y-axis) assuming different infall velocities for the El Gordo subclusters (x-axis). On the right y-axis, this probability is expressed in logarithmic scale (log10 P), and on the left y-axis, the probability is expressed in terms of the Gaussian equivalent number of standard deviations (χ). The solid red line shows χ accounting for the volume of the survey region in which El Gordo was observed. The solid black line shows χ considering both El Gordo and the Bullet Cluster (BC) in their respective survey regions (with χBC = 2.78). The error bars account for the uncertainty in the El Gordo mass. The dotted lines in the same colors represent more conservative estimates assuming the respective survey regions cover the whole sky, in which case χBC = 1.65 (Kraljic & Sarkar 2015).
The tension between the real Universe and the ΛCDM-theoretical universe is even greater when we take into account that El Gordo is not the only object with extreme properties that has been observed in the sky. Another example is the Bullet Cluster, with an estimated infall velocity of 3000 km/s. According to our analysis, the infall velocity of the El Gordo subclusters should be lower than 1800 km/s in order to be accommodated in a ΛCDM cosmology given the observations of both El Gordo and the Bullet Cluster in their corresponding discovery survey regions.
The tension would be reduced if we consider the probability of observing El Gordo and the Bullet Cluster in the full sky, and not just in their discovery survey regions. But this would imply that El Gordo and the Bullet Cluster are the only problematic objects for ΛCDM that have ever been observed, which is an unrealistic assumption. Other surveys – including full-sky surveys like Planck – have already found more clusters with outstandingly high masses. One of the most extreme examples is Abell 1758, with an estimated mass of 3.3 x 1015 Solar masses.
Considering these results, the following question arises: would it be realistic for El Gordo to have an infall velocity lower than 1800 km/s? Studies like Kim et al. (2021) claim that a configuration similar to that of El Gordo could be reconciled with an infall velocity as low as 450 km/s. However, in order to achieve this result in their statistical analysis, they imposed as a condition that only infall velocities that are expected from ΛCDM simulations should be considered. So it is not too surprising that they inferred an infall velocity for El Gordo that is below any significant tension with ΛCDM.
Up to this day, there are no hydrodynamical simulations of El Gordo that support such a low infall velocity. The most recent and thorough simulations of El Gordo were carried out by Zhang et al. (2015). In their best fit models that assume a mass of about 2 x 1015 Solar masses with a mass ratio of about 2 – similar to those obtained from the latest observations – they infer a preferred infall velocity of 3000 km/s to simultaneously reproduce its morphology, luminosity, temperature, and relative radial velocity. This infall velocity would imply that El Gordo is in 5.4σ tension with the ΛCDM theory (5.7σ when accounting for the Bullet Cluster). Other hydrodynamical simulations (Donnert 2014, Molnar & Broadhurst 2015) might not reproduce the properties of El Gordo as accurately as Zhang et al. (2015), but all their best fit models agree that infall velocities of 2500 km/s or even 2600 km/s are required in order to match its morphology and high luminosity and temperature to some extent. These are still in more than 5σ tension with the ΛCDM model, thus falsifying this theory of the Universe.
In conclusion, we found that even for the lower mass estimate yielded by the new analyses of the El Gordo mass, El Gordo still surpasses the 5σ falsification level at any plausible infall velocity. This result is consistent with the preliminary observations of the James Webb Space Telescope (JWST), which suggest that several high mass galaxies at very early epochs have already been found in its first data sample, galaxies which are in more than 3σ tension with the ΛCDM model. Independently, Haslbauer et al. (2022) showed that the distant candidate galaxies observed with the JWST have significantly more stellar mass than the galaxies formed in ΛCDM simulations at such early times. If the early JWST calibration is correct, this – together with the results of our analysis for the El Gordo cluster collision – would strongly imply that the formation and evolution of structures in the Universe is more efficient than predicted by the ΛCDM theory.
In The Dark Matter Crisis by Moritz Haslbauer and Pavel Kroupa. A listing of contents of all contributions is available here.
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(Guest post by Dr. Martin Lopez-Corredoira, who is a researcher at the IAC on Tenerife and at present Visiting Scientist at PMO in Nanjing (China). Martin has been publishing on the issue of cosmological models — we had covered his recent book in DMC Nr. 74. Very recently his Tenerife team published the research paper (“Virial theorem in clusters of galaxies with MOND“), and this contribution describes its contents. The setting: in Newtonian/Einsteinian gravitation, galaxy clusters show a mass discrepancy of a factor of a few hundred. In Milgromian dynamics (MOND), the mass discrepancy is nearly entirely removed, with only a factor of two in mass still missing. At least that is the current general concensus. Martin’s team from Tenerife has re-visited this problem pointing out that the boundary conditions matter, and that galaxy clusters may not even be missing mass in Milgromian gravitation. Martin’s research is supported by the Chinese Academy of Sciences President’s International Fellowship Initiative grant number 2023VMB0001.)
In present-day astrophysics, many lines of investigation support the existence of large amounts of non-baryonic dark matter (DM) particles in galaxies and in the Universe at large, the most obvious example being the asymptotically flat rotation curves of galaxies, which indicate the existence of massive DM haloes. Considerable fine tuning is required, however, to justify their observed properties, the most striking example possibly being the baryonic Tully–Fisher relation (McGaugh 2005). Because of this, over the years more than one proposal has been made to find alternative explanations not involving DM. In particular, it has been shown that a specific modification of Newtonian dynamics, known as MOND, is able to describe many observations without the need for DM in several astrophysical objects including (in increasing order of size) wide binary stars, globular clusters, dwarf galaxies, elliptical or spiral galaxies, including our Milky Way, satellites around galaxies, pairs of galaxies, groups of galaxies, gravitational lensing. MOND in the regime of very low accelerations creates a field (made by a ‘phantom mass’ that is not real matter though) which has an effect dynamically similar to the presence of non-baryonic DM in Newtonian gravity. Figure 1 shows as an example the galaxy cluster MACS J0717.
Figure 1: Galaxy cluster MACS J0717. Credit: NASA, ESA, CXC, C. Ma, H. Ebeling and E. Barrett (University of Hawaii/IfA), et al. and STScI.
However rich clusters of galaxies have been more problematic for MOND. A first problem is related to the offset between X-ray and weak-lensing distributions, like in the case of the Bullet Cluster. This is a problem for MOND because one would expect the phantom mass that mimics the role of the non-baryonic dark matter to be distributed around the baryonic matter traced by X-ray emission, and it is not the case here. Nonetheless, proposals to solve this MOND problem in terms of the existence of sterile neutrinos work (Banik & Zhao 2022, and references therein). The off-set of the neutrinos with the baryonic mass is explained because of an internal collision of two components of the cluster. Not a very elegant solution, because this forces MOND to admit the existence of some non-baryonic dark matter (although a known one, neutrinos, rather than a mysterious matter never observed), but these kinds of ad hoc solutions are not worse, and if anything they are better motivated from standard particle physics, than the usual ad hoc corrections in the standard ΛCDM cosmology. Moreover, precisely with the Bullet cluster and another massive cluster called “El Gordo“, there is a fast collision between individually rare massive clusters which is unexpected in standard ΛCDM cosmology and is ruled out at the 6.2σ confidence level in ΛCDM cosmology (Asencio et al. 2021), so apparently Bullet Clusters and other similar cases can be used more as an argument against the standard dark matter cosmological model than in its favour.
A second long-standing problem was the virial theorem in clusters of galaxies, which works for standard Newtonian gravity within the usual assumption of the existence of non-baryonic DM as predicted by ΛCDM models, but it had not worked for MOND till now: there was a deficit (by a factor around two) of predicted dynamical mass derived from the virial theorem with respect to observations. The usual explanation for this is that galaxy clusters are so massive and huge, that they capture sterile neutrinos which are elementary particles needed to explain why normal neutrinos change their mass. These sterile neutrinos add the factor of two in missing mass (in MOND a sterile neutrino needs to have a rest mass of about 11eV/c2, while in the standard ΛCDM model sterile neutrinos can be much lighter). The currently favoured MOND-cosmological model assumes that there is about 5 times as much mass in sterile neutrinos than in ordinary matter and thus “νHDM cosmological model” has the same expansion history as the standard ΛCDM model (Angus et sal. 2013,Katz et al. 2013).
In our work recently published by Martin Lopez-Corredoira et al. (2022), new analytical calculations of the virial theorem in clusters are developed, applying pressure (surface) corrections for non-closed systems and including recent calibrations of mass profiles, allowing free parameters to range within the observational constraints. It is shown that solutions exist for MOND in clusters that give similar results to Newton + DM within the range of parameters compatible with the known distributions of (only) baryonic matter. Figure 2 shows how well these new Newtonian calculations in which there is about 10 times as much non-baryonic dark matter than normal matter reproduce the data, and the paper demostrates that MOND can get a solution very close to the Newtonian one. This last theory does not even have sterile neutrinos, but accounts for the boundary conditions relevant for the galaxy clusters. Figure 2 and Figure 3 show how well these new MOND calculations reproduce the data.
Figure 2: This is figure 5 in López-Corredoira et al. (2022). Each data point is a galaxy cluster, represented by a colour in dependence of its redshift. The standard, dark-matter cosmological models are shown by the black solid line. These need a few hundred times more mass in exotic dark matter particles to be in the cluster than is observed in the hot X-ray emitting gas and in galaxies. The best power-law fit is shown by the black solid line (x is the variable on the x-axis, i.e. M500 in units of 1014 solar masses). The dashed red curve corresponds to Newtonian+DM theory (NFW is the mathematical form of the dark matter halo profile), and the MOND model for some parameters (without any additional sterile neutrinos) reproduces approximately this red line.Figure 3: This figure is not in López-Corredoira et al. (2022) but has been made for this contribution. It is as Figure 2 above except that the MOIND models are now plotted here as the red dashed line. The uncertainty ranges on the black line (the best fit to the data) are shown here in darker shade. Note that the MOND models are very similar to the Newtonian+DM models in Figure 2 and in fact lie closer to the best fit line. The MOND models have no contribution from sterile neutrinos (and of course also no dark matter).
Our results (López-Corredoira et al 2022). show that they can reconcile MOND with the virial theorem in clusters. This agreement is obtained when: 1) the pressure term is taken into account in the virial theorem, which gives a 10–15 per cent higher velocity dispersion of matter in the galaxy clusters for MOND than for Newton + DM; 2) we explore a range of possible parameters in the baryonic matter profile rather than adopting a fixed one. In particular for MOND, we predict velocity dispersions equivalent to Newton + DM by adopting an isothermal β model with β = 0.55–0.70, and core radii rc < 0.3*r500 (r500 is the radius of the sphere for which the average density inside it is 500 times the critical density ρc;; β is a parameter of the baryonic density distribution, namely: J(r)=(1+(r/rc)²)-1.5β), which is in agreement with the known observations. This can increase the velocity dispersion by another factor 10–15 per cent with respect to previous calculations.
This last effect is easy to understand in MOND: lower concentrations enhance the MOND effect because the galaxies spend a longer time during their orbits in the MOND regime of low (<a0) accelerations, i.e. in the outer regions of their clusters. Also, the greater pressure term for MOND is due to a lower concentration of gravitating matter (i.e. of the baryons = hot gas plus galaxies) than in the standard Newtonian plus dark matter models. Given that the dynamical mass is proportional to the third power of the dispersion of velocities, this means dynamical masses were 40–60 per cent lower in former studies, and this would explain the discrepancies found previously.
Thus, at least numerically speaking, the problem is solved and one can say that the virial theorem in clusters can be explained with MOND without needing to add extra unseen matter into the clusters.
In The Dark Matter Crrisis by Moritz Haslbauer and Pavel Kroupa. A listing of contents of all contributions is available here.
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When building a LEGO death star, one would require more blocks and more time to assemble a big death star, and less time for a smaller death star. This is not the case for building real elliptical galaxies though. Just after the Big Bang, nature made bigger galaxies more rapidly and earlier. Trying to understand how this was possible has been plaguing astrophysicists since decades. We addressed this problem in our recent publication “The formation of early-type galaxies through monolithic collapse of gas clouds in Milgromian gravity” by Eappen et al. (2022, MNRAS). Here we outline the problem and its solution.
Synopsis of the text below: Elliptical galaxies formed very rapidly and very early, and the more massive, the quicker and earlier they formed. This is in contradiction to dark-matter based models of galaxy formation, but can be explained easily in a Milgromian universe. We also explain which types of galaxies are the most common, and how this fits into the models of galaxy formation and evolution.
A typical present-day elliptical galaxy is shown in Fig. 1. When it was forming it must have been an extremely rapidly changing brutally extreme region of the new space time, in terms of the amount of mass piling up incredibly fast and the destructive, quasar-like radiation field coming from it. This is where super-massive black holes formed (read “Supermassive black holes: monsters in the early Universe” based on Kroupa et al. 2020). This is what the calculations in Milgromian gravitation (i.e. MOND) tell us. Models of the formation of galaxies in the popular dark-matter theory fail to account for these galaxies.
Fig.1: Elliptical galaxy IC 2006. It is about 20.2 Mpc distant and has an inertial baryonic mass of about 2×1010 MSun (Trinchieri et al. 2015). ESA/Hubble & NASA Image acknowledgement: Judy Schmidt and J. Blakeslee (Dominion Astrophysical Observatory). Note that the image is not related to science release content. Science acknowledgement: M. Carollo (ETH, Switzerland)
What sort of galaxies are out there?
Lets take a step back: broadly, there are rotationally supported galaxies – the disk (or “late-type”) galaxies, and there are pressure supported galaxies – the elliptical (or “early type”) galaxies. In “pressure supported” galaxies, the stars are on randomly oriented and randomly tilted orbits, so the whole galaxy looks spheroidal (e.g. as in Fig. 1). Rotationally supported galaxies, like our Milky Way, are very flat disks and the random motions between the stars are very small compared to the rotation speed, and compared to the random motions between the stars in an elliptical galaxy of the same stellar mass. The stars and gas orbit about a common centre on nearly circular orbits and in nearly one plane. Disk galaxies are forming stars while elliptical galaxies are essentially void of star formation. Disk galaxies can form stars because the gas they contain can cool to form molecular clouds. Elliptical galaxies also contain gas, but it seems to be kept too hot for star formation. The tuning-fork classification scheme for galaxies (invented by Reynolds and Jeans, and not by Hubble – see DMC 78 – the wikipedia page needs correction on this), gives the finer details of galaxy classification. A more modern classification scheme is the deVaucaoleurs class-system on which is based the approximate Hubble class T (see this Wikipedia description).
Now, it might be perhaps surprising for some readers, and certainly for many extragalactic astronomers (!), that elliptical galaxies are very much the exception. For example, the survey by the Parisian/Meudon group around Francois Hammer, Delgado-Serrano et al. (2010) , informs us that among all galaxies containing more than about 1010 MSun in stars, only some 3-4 % are ellipticals, the rest being rotationally supported disk galaxies (some have little gas wile others are currently undergoing encounters and so appear distorted, see Fig.2 below).
Fig.2 (fig.5 in Delgado-Serrano et al. 2010): the types of galaxies containing more than about 1010 Msun in stars and their frequency of occurrence today and about 6 Gyr ago. Note that the fraction amongst all galaxies of elliptical (“E”) galaxies does not change significantly. Note also that at both times, about 96-97% of all galaxies are disk galaxies, with a larger fraction of perturbed galaxies 6Gyr ago due to a larger frequency of encounters then. These do not form present-day E galaxies because the fraction of these does not increase.
The remarkable result obtained by these authors is that this tiny fraction of elliptical galaxies was the same about 6 Gyr ago. This means that the population of elliptical galaxies did not increase with time, as would be expected if they form from disk galaxies that merge, as ought to be the case in the highly popular dark-matter model of galaxy formation and evolution. The observational fact that star-forming (i.e. gas-containing) rotationally supported (i.e. disk) galaxies completely dominate the galaxy population at any mass is already well known since the 1980s. Thus, in an important review, Binggeli, Sandage & Tammann (1988) document (see their fig.1) that dwarf elliptical (dE) and elliptical galaxies are a negligible few-per cent fraction of the whole galaxy population in the field, and in galaxy clusters dE’s contribute more but elliptical galaxies are also very rare. The larger fraction of dE galaxies in galaxy clusters is naturally understood by them being old tidal-dwarf galaxies that formed in the dense environment when disk galaxies interacted there producing tidal tails within which the new little “tidal tail dwarf” galaxies formed, as nicely argued by the Japanese Okazaki & Taniguchi (2000). How tidal tails are created in Milgromian hydrodynamical simulations of the past encounter between the Milky Way and Andromeda producing the Disks of Satellites (or satellite planes) around the Milky Way and Andromeda have been shown by the remarkable pioneering work led by Indranil Banik et al. (2022), and corresponding simulations without gas had been explored by Michal Bilek et al. (2018) who also show the galactic warps to emanate from this past encounter about 8-11 Gyr ago.
The observed disk galaxies do not fit the model galaxies in the dark-matter models:
Incidentally, talking about disk galaxies: the dark matter models of disk galaxies absolutely do not fit the observed disk galaxies. Apart from the dark matter models of disk galaxies being too roundish (Haslbauer et al. 2022a), the observed population of disk galaxies has many barred galaxies, i.e., thin disk galaxies that have, in the inner maybe 1/4th of their diameter, a straight bar. That the dark-matter based cosmological simulation completely and utterly fail to account for the large number of barred galaxies has been noted recently by Reddish et al. (2022). These authors point out that the model galaxies are too dark-matter dominated in their inner regions such that the bar instability cannot develop in them. In the real observed Universe, the disk galaxies do not contain dark matter and thusly they can readily develop bar instabilities, e.g. upon a weak perturbation from a passing galaxy. That real observed disk galaxies do not contain dark matter has been demonstrated by the bar rotation speed of the observed barred galaxies being too fast compared to model galaxies that have dark matter: Roshan et al. (2021) show that the observational data falsify dark matter with much more than 5 sigma confidence. Dark matter thus indeed does not exist since it is impossible in the dark matter cosmological models to build disk galaxies lacking dark matter.
But back to the ellipticals:
As seen above, it is observationally established that elliptical galaxies comprise not more than a few per cent of the whole galaxy population. Only in the most dense and innermost regions in the most massive galaxy clusters do elliptical galaxies contribute maybe half the population (see fig.8 and 9 in Dressler 1980). These are very rare environments though.
It is thus evident that any theory of galaxy formation and evolution which leads to a large fraction of elliptical galaxies will be wrong. This applies, one expects, to all theories of galaxy formation and evolution that rely on mergers leading to growth of mass. We explicitly tested if the dark-matter based models can account for the observed age-properties of elliptical galaxies (see below) finding these models to be completely ruled out with more than 5 sigma confidence (Eappen et al. (2022, MNRAS).
One of us (PK) made a little in-official survey recently and some years back: I asked observational astronomers at various institutes what they think: which type of galaxy dominates the counts? Most usually replied that the elliptical galaxy is the most common type of galaxy.
Why do modern-day observational astronomers have such a completely wrong impression of what is out there? What is the reason for this massive cognitive dissonance?
The reason for this quite massive cognitive dissonance lies, I think, in the LCDM model easily making ellipticals (in terms of their structure, but not in terms of their observed extremely old ages and quick formation), but can hardly make thin disk galaxies. Young astronomers grow up in an academic environment in which the LCDM model is the only model of galaxy formation and evolution they ever encounter, and the many talks by awe-inspiring and blindingly bright luminaries of the LCDM world and their huge army of workers (PhD students and postdocs – the luminaries have all the money to hire and “teach”, after all) then instil the notion that ellipticals rule the Universe.
The reason why the LCDM model easily makes elliptical galaxies in terms of their structure is simple: in the dark matter models galaxies grow in mass mostly through random mergers and mergers destroy thin disk galaxies. Crashes make things rounder: for example, a car would become more spherical if it would undergo a series of crashes on the German autobahn. So the fact that one mostly sees non-spherical cars implies that crashes are rare.
We tested this explicitly on the most modern cosmological simulations showing that the LCDM model results in a population of galaxies that is wrong by more than 5 sigma confidence: the real observed vast number of thin disk galaxies stands in opposition to the many model LCDM elliptical galaxies (Haslbauer et al. 2022a). Haslbauer et al. (2022a) thus demonstrated another terminal failure of the dark matter models. As a typical example: Our Milky Way has a disk diameter of about 50 kpc (yes, stars are forming at a distance some 25 kpc away from the centre, our Sun being at about 8.3 kpc distance, see e.g. Zhou, Huang & Chan 2023), while the disk thickness is about 500 pc (see e.g. Zhou, Huang & Chan 2023). A typical disk galaxy is thus a truly ultra-thin, nearly razor sharp flat disk with thickness to diameter ratio of 1 to 100. Such disks are very sensitive, and many are slightly warped due to weak perturbations from nearby galaxies. Mergers are a no-go for keeping such ultra-thin disks en masse.
To summarise:
The dark-matter-based cosmological models fail on three accounts (the failure is by more than 5 sigma confidence each):
They cannot account for the observed galaxy population being made up of some 90-95 % of rotationally supported thin disk galaxies (Haslbauer et al. 2022a).
They make thick disk galaxies that do not have bars, while between 1/3rd to 2/3rd of all observed disk galaxies have a bar (Reddish et al. 2022) which is rapidly turning rather than being slow as expected if dark matter were to be present (Roshan et al. 2021).
They lead to most galaxies being spheroidal, i.e. structurally similar to observed elliptical galaxies with these taking long to form through many subsequent mergers, in contradiction to the observed very rapid and early formation of the observed elliptical galaxies (Eappen et al. 2022).
But why did the real elliptical galaxies form so quickly? And how could the more massive ones form faster and earlier than the less massive ones?
And so here we are at the core of the mystery:
According to the widely believed dark matter models, massive galaxies (u.e. mostly ellipticals in these models) take much time to grow to their mass through crashes. In the models, low-mass galaxies form first, and then the star-forming galaxies merge, such that a present day model elliptical would contain stars that formed over many Gyr in the merger precursors. But observed, real elliptical galaxies formed very fast, and very early. It even seems that they may have been the first galaxies to have emerged after The Beginning. In fact, the incredibly short time-scales of the formation of the real observed elliptical galaxies appear to be consistent with each of them forming from the single collapse of a giant post-Big-Bang gas cloud.
The observational studies show that massive early-type galaxies (an example is shown in Fig.1) even form over a shorter timescale compared to less massive early-type galaxies (Yan et al. 2021 and references therein). This rapid formation trend was given the name “downsizing” by Cowie et al. (1996) where the less massive galaxies have an extended star-formation history (more time to assemble). This downsizing timescale would be approximately 0.3 Gyr for a galaxy of mass 1012 MSun.
How reliant are the early and short formation time scales of elliptical galaxies?
The seminal work by Thomas et al. (2005) established downsizing using measurements of “alpha element abundances” and metallicities for 124 elliptical galaxies: The high “alpha-abundances” and high metallicities mean that most stars in such galaxies formed before supernovae type Ia contributed much iron to the gas, and the high metallicities imply that the formation of all the stars was incredibly intense, i.e., that elliptical galaxies formed with very high star-formation rates (SFRs), much higher than the Milky Way’s present SFR of about a few Msun per year (e.g. Zhou, Huang & Chan 2023).
McDermid et al. (2015) calculate model spectra of galaxies and compare these to observed spectra of a few hundred elliptical galaxies finding essentially the same result as Thomas et al. (2005) above with systematically slightly longer formation time scales (see Yan et al. 2021 for details). The results of Thomas et al. (2005) and McDermid et al. (2015) are valid for the inner regions of elliptical galaxies. Maybe these formed rapidly, and the outer parts added later?
Salvador-Rusinol et al. (2020) and Salvador-Rusinol et al. (2022) test, using their observations, if elliptical galaxies might contain a significant addition of stars after the fast and early formation of their inner regions, and demonstrate that any later addition was very minor.
Thus downsizing is rather very well confirmed (i.e. elliptical galaxies formed very rapidly and very early, and the more massive ones formed earlier and quicker) and so we are at the following stage – we need to study a very different new model (radically different to anything resembling the failed dark matter models) that needs to fulfil a number of constraints:
Since the dark-matter models are not relevant for the real Universe (they have been falsified with much more than 5 sigma confidence, see previous DMC blogs), we need an entirely new theoretical model,
This model should be based on MOND, because all tests performed to-date indicate that self-gravitating structures in the real Universe behave as expected in MOND (even star clusters: Kroupa et al. 2022).
MOND is a gravitational theory rather than a theory of modified inertia (cf. Kyu-Hyun Chae 2022).
The observational fact that more massive elliptical galaxies formed more rapidly than less massive ones suggests a model based on the collapse of a gas cloud: given the same initial radius, a more massive cloud will collapse faster than a less massive one.
Since elliptical galaxies are essentially not rotating (they may have a weak rotation, but their ellipsoidal shape is given by the stars in them moving on randomly oriented oribts, i.e., the galaxy is pressure supported), the initial gas clouds need to be non-rotating. As an aside: that the collapse of a rotating post-Big-Bang gas cloud under Milgromian gravitation forms a disk galaxy with an exponential radial disk and all the other correct properties has already been shown by us through computer simulations (Wittenburg et al. 2020). And, that how stars form from the gas is physically modelled in the MONDian simulation code PoR (Lueghausen et al. 2015; Nagesh et al. 2021) adequately, has also already been shown by us (Nagesh et al. 2022).
Our models:
In our work (Eappen et al. 2022: “The formation of early-type galaxies through monolithic collapse of gas clouds in Milgromian gravity“) we model, using PoR, the collapse of non-rotating post-big-bang gas clouds in MOND to study the properties of early-type galaxies. Remarkably, they are found to be very close to the observations !
What did we do?:
We set up initial (i.e. post-Big-Bang) gas clouds with masses ranging from 0.6×109 to 1.0×1012 MSun (for comparison: our Milky Way has today in total 4.2×1010 MSun in stars: table 5 in Zhou, Huang & Chan (2023), and for each mass, clouds with initial radii of 50 to 500 kpc are initialised as homogeneous non-rotating gas spheres (the same type of simulations but for initially rotating gas clouds form disk galaxies with the observed properties: Wittenburg et al. 2020). We then analyse the star-formation history and the radii and rotation rates of the formed galaxies. For a given mass, the collapse time and thus the star-formation time scale goes faster for the initially smaller clouds. For a given initial radius, both go faster for the more massive models. By matching the observed star-formation time scale as measured by Thomas et al. (2005) with the model ones, we deduce that the typical observed elliptical galaxy of any mass would have formed as a monolithically collapsing non-rotating cloud with a radius near 500 kpc.
Results:
We therefore find that the timescales needed to build these massive galaxies are similar to those of the observed elliptical galaxies provided the physics of the Universe is indeed Milgromian and the collapse starts from initially not rotating gas clouds that have radii near 500 kpc. That is, elliptical galaxies are the very rare outcome of monolithic gas cloud collapse without rotation, and the collapse occurs on a free-fall time in Milgromian gravitation. This naturally explains the observed down-sizing: the more massive clouds must collapse faster if all clouds begin with the similar initial radius of 500 kpc. This bears important constraints on the cosmological initial conditions of the MONDian universe that we are now contemplating. Fig. 3 below shows the star-formation histories (SFHs) of the more massive models.
Fig. 3a: The star formation histories of the collapsing clouds with initial radii of 500 kpc. The x-axis is the time since the Big Bang for a part of the low-density Universe where such clouds (non-rotating and with an initial radius of 500 kpc) would be collapsing. The models have masses (from top to bottom) 1×1012, 7×1011, 6.4×1010, 5×1010, 3×1010, 1×1010 MSun . The vertical thick black line shows the time relative to the Big Bang (gauged using the results of Thomas et al. 2005) when the first stellar particle forms. For details see Eappen et al. (2022).
Fig. 3b: As Fig. 3a on the left but for a high-density part of the Universe. Note that the first stars would have formed in the most massive galaxies at about 1.7 Gyr after the Big Bang. Since this is an average for the high-density Universe it is to be expected that in peak-density environments the first stars would be forming much earlier still. For example: the 1×1012 cloud (model e40) forms the first stars at its centre about 1.7 Gyr after the Big Bang and reaches a peak SFR near a few times 104 MSun/yr about 2.3 Gyr after the Big Bang. Such high SFRs have been observed in the young Universe (at a redshift near 4.8, i.e. about 1.5 Gyr after the Big Bang, e.g. fig.9 in Nguyen et al. 2020).
As the stellar particles in the collapsing gas clouds build up following the SFHs shown in Fig. 3, the gas is consumed. After a few Gyr the star formation rate has decreased to a negligible value and the whole galaxy is done. The so-formed galaxies have final radii that increase with the mass of the galaxy in stars in the same way as the real observed galaxies, but the model galaxies are systematically more compact by a factor of about three (fig.7 in Eappen et al. 2022). Our calculations also show that the formed galaxies would become precisely as large as the observed galaxies if only two such collapse-formed galaxies merge. Thus, if the “pristine” elliptical galaxy forms from a free-fall collapse of an initially non-rotating post-Big Bang gas cloud with a radius near 500 kpc, then the radii of the observed elliptical galaxies in the real Universe come out correct if only two of such pristine galaxies merge.
This suggests that most elliptical galaxies form not as a single object, but as a pair or even triple system, e.g. in the inner region of a forming galaxy cluster. The central E’s then merge through dissipational processes (tidal and dynamical friction through the stars [not dark matter]) to become the final galaxy observed today. Those rare cases that do not merge end up being very compact today, and are in fact next-to-identical to the “compact relics” (e.g. Trujillo et al. 2014) as we show in an associated paper (Eappen & Kroupa, in preparation).
The above observational results and Milgromian collapse models show elliptical galaxies to have formed perhaps as the first objects in the Universe. This has implications for observations of the very high redshift (z>10) Universe. The JWST is now providing such data (see DMC 79). In the seminal first paper studying structure formation in a Milgromian universe, Sanders (1998) (see also Sanders 2001) already predicted that “objects of galaxy mass are the first virialised [i.e. gravitationally stable] objects to form (by z=10), and larger structure develops rapidly. At present, the Universe would be inhomogeneous out to a substantial fraction of the Hubble radius.”
Implications for the very early Universe and JWST observations:
Comparing our formation timescales to those of the real elliptical galaxies, we find that the first stars in these early-type galaxies would have formed much earlier than what we have seen until JWST data came out. JWST recently found a galaxy, GLASS-z12 (originally GLASS-z13) approximately at a redshift of 12.4 (Fig.4 below; Naidu et al. 2022) marking it one of the earliest and most distant galaxies ever discovered.
Fig.4: The GLASS-z12 (originally GLASS-z13) galaxy is smaller in size than the Milky Way. Photo: NASA/CSA/ESA/STScI.
These early results obtained by the JWST reveal that this galaxy formed just 200 million after the Big Bang and there are more hidden massive galaxies yet to be found at redshift greater than 10. GLASS-z12 had, at that young age, already a stellar mass of about 109 MSun and this causes significant problems for the dark-matter based models in which such massive galaxies could not yet have formed through mergers (Haslbauer et al. 2022b).
This is consistent with our work also. We showed that in a Milgromian Universe, elliptical galaxies form through the rapid monolithic collapse such that they grow in stellar mass on a free fall time (Fig. 3 above). Nevertheless, the incredibly early formation of massive galaxies (only some 200 Myr after the Big Bang, e.g. GLASS-z12) poses fundamental constraints on any cosmological model.
The problem we are tackling now: can a cosmological model based on Milgromian gravitation lead to such rapid formation of early galaxies? Can it yield the present-day observed population of galaxies which is dominated by thin disk galaxies? What are the initial conditions for a Milgromian cosmological model to achieve this?
In The Dark Matter Crisis by Moritz Haslbauer and Pavel Kroupa. A listing of contents of all contributions is available here.
In disagreement with dark-matter-theory, dwarf galaxies in the Fornax Galaxy Cluster are void of dark matter. They behave exactly as expected from MOND. The inequality of gravitating mass and inertial mass of galaxies is indepedently confirmed using rotation curves of field disk galaxies.
Dwarf galaxies are supposed to be the most dark-matter dominated galaxies in the Universe. At least according to the standard Einsteinian/Newtonian-gravitation and dark-matter based LCDM model of galaxy formation (Battaglie & Nipoti 2022). In this LCDM model, the dark-matter-dominated dwarf galaxies must, if they are satellite galaxies, be distributed spheroidally around their host galaxies. But several studies focussed on the dwarf galaxies in the nearby Universe (the Local Group and its vicinity) have already shown that the LCDM model fails to explain many of their observed properties, in particular, that most of them are in disk-like configurations around their host galaxies (Pawlowski 2018; Pawlowski & Kroupa 2020; Pawlowski 2021; Pawlowski 2021).
Concentrating only on their dark matter content, such dwarf galaxies will be protected, though their large and massive dark matter halos that surround them, from tidal effects if they orbit through a cluster of galaxies. It is well known since at least 2004 that dwarf galaxies cannot be much affected by tides in LCDM theory. Citing from Kroupa et al. (2010, Sec. 2.8): “… the inner region of a satellite is only affected by tides after significant tidal destruction of its outer parts (Kazantzidis et al. 2004).” Therefore, for the visible part of the galaxy, which is the innermost part of any galaxy’s dark-matter halo in the LCDM model, to be affected/perturbed/distorted by tides, the galaxy must first be rid-of most of its dark matter halo. This takes many orbits such that only a very small fraction of observed dwarf galaxies can show tidal deformation if dark matter halos exist. The window of opportunity for catching a dwarf galaxy in this perturbed-by-tides state is brief: When most of the dark matter halo has been removed, it only takes about one more orbit for the dwarf galaxy to be completely destroyed.
By counting the number of observed dwarf galaxies that show signs of tidal deformation, we can thus test for the existence of dark matter: if too many dwarfs are distorted, then dark matter does not exist.
In this recently published work (Elena Asencio, Indranil Banik et al. 2022, MNRAS, in press), we present a new line of evidence for the unsuitability of the standard dark-matter-based models to describe these objects. This study, lead by Elena Asencio, is a very extensive analysis of the statistics of the perturbations of dwarf galaxies in the Fornax Cluster of galaxies, and is a result of a multiple-year collaboration between researchers working at the University of Bonn, the University of St. Andrews, the European Southern Observatory in Chile, the University of Oulu in Finland, the University of Groningen in the Netherlands, and Charles University in Prague.
The dwarf galaxies of the Fornax Cluster are subject to the gravitational effects of the cluster environment. In the standard (Newtonian-gravity) dark-matter models, the dwarf galaxies are surrounded by a dark matter halo, so they should be mostly shielded from these gravitational forces. However, many of the Fornax dwarfs are observed to have distorted morphologies, which highly contradicts the LCDM-model expectation – as the results of this study show.
The above image shows the Fornax galaxy cluster. This is fig.9 in Venhola et al. (2018): “Magnification of Field 5 with the detected objects and masks (black circles) overlaid on the image. The yellow points and red symbols correspond to the initial detections of our detection algorithm, and the objects that pass the A_IMAGE > 2 arcsec selection limit, respectively. Aladin (Bonnarel et al. 2000) was used for generating the image. The image is best viewed in color on-screen.“
We performed a similar test assuming a MONDian model (i.e. based on Milgromian gravitation without dark matter), which turned out to be very consistent with observations. In MOND, the dwarf galaxy is surrounded by a “phantom dark matter halo” (e.g. Lueghausen et al. 2013; Oria et al. 2021, ApJ) when it is far away from the centre of the galaxy cluster. This phantom dark matter halo is not real, it is merely Newtonian-speak to describe the true Milgromian potential of the galaxy. This potential is deeper and more extended when the dwarf is nearly isolated. When the dwarf plunges into the cluster, this phantom dark matter halo disappears. This is merely the mathematical consequence of the generalised (Bekenstein/Milgromian) Poisson equation and only means that the true Milgromian potential becomes less deep and shrinks. In other words, the galaxy’s gravitating mass is reduced, while its inertial mass remains the same. In this naked state, every dwarf galaxy is susceptible to tides, and so many dwarf galaxies are expected to show signs of distortion. It can happen that the dwarf is completely destroyed, but this would be a rare event and would remove dwarf galaxies quickly that are on orbits that take them very deep into the inner parts of the galaxy cluster. As the dwarf then orbits out from the central region, its phantom dark matter halo grows back (again this is merely a mathematical consequence) and the dwarf galaxy stabilises, having regained its gravitating mass which is much larger than its inertial mass in Milgromian dynamics. This process of loosing the phantom dark matter halo and regaining it as the satellite galaxy orbits within its galaxy cluster or around its host galaxy has been studied in detail in “The dynamical phase transitions of stellar systems and the corresponding kinematics” by Xufen Wu & Pavel Kroupa in 2013.
We thus have a beautiful convergence of LCDM failures – And at the same time, we also have a beautiful convergence of verifications of MOND:
Dwarf satellite galaxies are in planes around their host galaxies, like planetary systems around their stars, and dwarf galaxies have no dark matter.
Both of these properties show dark matter to not exist (and thus the entire LCDM model to be ruled out), and, at the same time, both are well understood if gravitation is Milgromian (see also DMC Blog 49). Both are well understood (i) because dark matter does not exist but the “dark-matter” content of dwarf galaxies is merely due to their orbit-dependent phantom dark matter halos, and (ii) because the planes of satellite galaxies are completely naturally produced when major gas-containing galaxies interact, like what happened between the Milky Way and Andromeda about 10Gyr ago (Bilek et al. 2018; Bilek et al. 2021; Banik et al. 2022).
Is there independent evidence for the waning and waxing phantom dark matter halo around galaxies predicted by MOND?
Haghi et al. (2016, MNRAS) had suggested that this may be nicely tested using rotation curves of galaxies: As stated above, if isolated, the gravitational mass of the galaxy is much larger than its inertial mass. Mathematically this spells out as it having a logarithmic Milgromian potential, which is synonymous to it having a phantom dark matter halo, the mass of which that is within R increases proportionally with distance, R, in Newton-language [Mphantom(<R) propto R]. This is demonstrated in the figure below (Fig.1 in Haghi et al. 2016).
Fig.1 from Haghi et al. (2016): The rotation speed, V, around the centre of a Milky-Way like galaxy as a function of distance, R, from the centre. An isolated galaxy has a flat rotation curve (uppermost solid line), but when other galaxies are placed in its vicinity they exert an external field across the galaxy leading to the external field effect (EFE) which leads the rotation curve to fall. The lowest thin curve is the pure-Newtonian (i.e. Keplerian) rotation curve when all of the phantom dark matter halo of the galaxy has vanished due to a strong EFE – the galaxy being “naked”. The strength of the EFE is described by the external acceleration ae.
The rotation curve is perfectly flat to very large R. Place this same galaxy into a region where there are other galaxies, then Mphantom will be smaller, and the rotation curve will fall. Thus Haghi et al. (2016, MNRAS) wrote the paper “Declining rotation curves of galaxies as a test of gravitational theory” pointing out that a signal is evident. And, using this approach and much improved data, extremely strong independent evidence for the breaking of the equality between inertial mass and gravitating mass described above and as predicted by MOND has thereafter been published by Chae et al. (2020, ApJ) and Chae et al. (2021, ApJ). Clearly, this constitutes a very major progress in fundamental physics.
After attending the “HowTheLightGetsIn” Festival in Hay on Wye in Wales, June 2nd-5th, 2022, I was asked by the Institute for Art and Ideas (iai) to draft a text capturing the current state of the dark matter science. It was published on July 12th, 2022. Here it is:
While composing the iai text the question returned about how much money is being spent each year on a) salaries of all dark matter people, b) dark matter searches. The draft I had sent to iai (the above text) was immediately accepted and I did not have the opportunity to include the following updated estimate into it. But here it is:
My estimate: There are 12131 IAU members.
If half work on dark matter and if the average salary is 40000 USDollars per year, we have 242 million dollar per year being spent on dark matter research.
If there are currently ten dark matter searches, each costing on average 50 million per year, we have 500 million dollars per year (much of it on salaries for engineers, equipment, astronauts).
That is, the tax-payer is expending something like three-quarter of a billion dollars each year on largely useless “research”. A large fraction of scientific funding thus meanwhile goes into an activity which is based on pure belief contrary to evidence. One might interject that some of the experiments lead to the development of new technology. This would be equivalent to the situation where a state organises, using tax-payer money, a job-programme which employs people to dig many holes. The useful aspect of this would be that the unemployment rate would decrease, but the measure would leave no lasting benefit. In terms of the dark matter problem, it would be advisable to support research projects on non-falsified theories which lead to innovative technologies. Another way to express the above is to say that our modern, 21st century technological civilisation is essentially actively funding religion camouflaged as science with the above amount.
The dark-matter based models were clearly ruled out already in 2010 (read “Local-Group tests of dark-matter concordance cosmology . Towards a new paradigm for structure formation“) and definitely falsified in 2012 (read “The Dark Matter Crisis: Falsification of the Current Standard Model of Cosmology“). Today, ten years later, ample time has passed even for the dimmest scientist to be able to catch up. Given that the arguments against dark matter have not been shown to be invalid, and have in fact multiplied manyfold (see the iai piece above), it is simply not to be understood from a rational point of view why we keep expending so many valuable resources into a falsified theory while, at the same time, suppressing a highly interesting and successful alternative. The scientists who continue pushing for this falsified dark-matter theory are hurting the sciences and are, by ignoring the falsifications, being unscientific. They appear to behave more like ancient Egyptian priests who fervently guard their particular god(s) to thrive on the citizens by faking the ability for communicating with these imaginary deities.
What keeps this system going? The LCDM model is a gold of mine for those, the “LCDM priests”, who are able to sell the dark matter and dark energy stories to the funding agencies. An impression of how this works can be gleaned by watching the Golden Webinars in Astrophysics (see e.g. Post 65). An excellent example of the process is evident the time following 1:13:18 in the Golden Webinars in Astrophysics by Martin Rees as a consequence of Martin Rees suggesting that the non-detection of dark matter is trouble.
Furthermore, the LCDM model is guarded by suppressing fundamental empirical evidence: David Merritt eloquently documents how virtually all important modern textbooks fail to report essential information on galaxies (see Table 1 in Merritt 2017). From my own personal experience I know of significant mobbing within universities and general massive discouragement of young researchers against touching MOND. More than one student working with me have told me that it was recommended by other very senior researcher that they not work with me. When I was younger, I was too told that one may publish on MOND, but only to show it is wrong. It appears that this “guiding” by senior researchers of younger ones may have contributed to the long list of flawed such claims (“The List of Messups” or “The List of Shame”, Post 70). A classical example of continued mis-representation of MOND is the repeated claim that the Bullet Cluster falsifies MOND (this was shown to be wrong already by Angus, Famaey & Zhao 2006, MNRAS ), and a present-day example can be found in the Introduction of a MNRAS publication which dismisses MOND altogether but ends up discovering a trivial MOND result.
It has thus become a perpetually repeating cycle: young scientists are, in nearly all research institutions, not confronted with the essential information, and at best learn about it in the context of fringe science, something better not to touch if a career is desired. They need a post-doctoral or better position, or the one or other prize. To ensure success they do what is needed. In this way the scientific system appears to have become corrupt: despite being ruled out by the evidence (see the iai composition above), dark matter has come to be seen as a non-exotic and established part of physics. For the benefit of ones own career one sticks with dark matter rather than following the “fringe evidence”.
This text is my (Pavel Kroupa’s) responsibility only.
In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.
This is a guest post by Dr. Indranil Banik (past Alexander von Humboldt Fellow in the SPODYR group at Bonn University and now at Saint Andrews University) on a comprehensive 150 page review of MOND.
The Banik & Zhao (2022) paper is an invited review for the journal Symmetry, in particular for their special issue on modified gravity theories and applications to astrophysics and cosmology. Dr. Banik consulted the community widely and incorporated many comments and suggestions into the review, including several from the referees.
First comes a preamble, followed by the guest post:
Preamble by Pavel Kroupa:
How can a theory be assessed in terms of us (i) trusting it to provide a physical model of a phenomenon we can comprehend rationally (i.e. in terms of mathematical language) and (ii) perhaps even more importantly, trusting it to allow predictions that we need (e.g. to send astronauts into space).
One possibility of how to assess theories in terms of the above two points was approached in two previously published invited reviews, Kroupa 2012 and Kroupa 2015. In these I analysed the dark-matter based theories that rest on Newtonian/Einsteinian gravitation being valid also on the scales of galaxies and beyond. In the 2012 paper, I introduced a visualisation and test of how theories fare by plotting the evolution of confidence in the theory with time. Each time a given theory fails a test, confidence is lost, e.g. by 50 per cent (to be conservative). A total falsification would be achieved if a test or sum of independent tests achieves a threshold where the confidence remains at one in one point seven million. This is the “5sigma” threshold that signifies a discovery, e.g. of a particle (meaning that the hypothesis that the particle does not exist has a remaining confidence of 1 in 1.7 million, the non-existence of the particle therewith being falsified with a confidence of 5sigma). I concluded that the dark-matter-based models are falsified with more 5sigma confidence (i.e. the discovery is made that the dark matter models are not valid). The dark-matter-based cosmological models are thus not viable descriptions of the Universe. Blog Nr. 51 shows this graphically.
Put in other words: if you would send out astronauts to another part of the Milky Way and if you believe in the dark matter theories, then the astronauts have a chance of below 1 in 1.7 million to reach the destination and to live. Obviously we want to raise the chances of hitting the target. That is why we need a different theory. MOND appears to be such a theory. As an astronaut with a desire to live, I would navigate my ship according to Milgrom’s equations of motion, and not Einstein’s ! This is true because application of the “confidence graph” to MOND shows that MOND has not lost confidence (Kroupa 2012).
Nevertheless, the scientific establishment has a great inertia, and the majority of cosmology-related scientists work on the basis of belief (that dark matter exists and these theories remain valid despite the evidence), implying that much effort and taxpayers money needs to be kept being wasted in showing they are ruled out using additional tests. This is very necessary because the scientific establishment can just keep on ignoring results as long as the majority of scientists go along with this (see the previous blogs here on this issue). The weaker majority can be shepherded into a main-stream behaviour of ignoring a falsification through pressure and power exerted by “ΛCDM priests”.
The new very major and highly detailed review by Banik & Zhao, described below, is therefore essentially needed to keep up an opposing pressure such that, hopefully, a few very talented and bright researchers can break away from the dark matter mainstream. The more scientists that show brightness, the better. This review also updates us on the performance of MOND.
Indranil Banik writes:
One of the great mysteries in astrophysics today is why galaxies rotate so fast in their outskirts compared to the circular velocity that we expect from applying Newtonian theory to the distribution of visible stars and gas. This flat rotation curve problem has been around for fifty years, but there is still no consensus on the solution. More generally, astronomical observations on a range of scales imply that there must be more gravity than classical theory predicts based on the directly detectable mass. This missing gravity problem could indicate the presence of large amounts of undetected mass (dark matter), a breakdown of our gravitational laws, or some combination of both. In this review, I considered the standard cosmological paradigm (ΛCDM) and Milgromian dynamics (MOND) as the best-developed alternative that has been around for almost forty years. I focused on all major areas of astronomy where the observations are reasonably accurate and different outcomes are expected depending on which of these models is correct. I also considered some future tests in Section 11. Other alternatives to these two approaches are briefly discussed in Section 3.6 (which covers superfluid dark matter and emergent gravity), but I conclude that it is highly unlikely for any model beyond ΛCDM and MOND to ever explain all the presently available evidence. I therefore focused on these two paradigms.
To assess which works better, I used a 2D scoring system developed with my co-author Dr. Hongsheng Zhao, also at Saint Andrews. One of these dimensions is the usual assessment of how well each theory matches astronomical observations of a particular kind, e.g. data from strong gravitational lenses. I assigned a score between –2 and +2 based on my assessment and that of other researchers. The other dimension used to score each theory against each test is the flexibility of the model when applied to the relevant observations. A strong a priori prediction would lead to a score of –2. At the opposite extreme, a score of +2 represents situations where the theory can explain any plausible data, i.e. observations that are plausible based on prior knowledge but without the benefit of the theory. The use of this second dimension to the scoring system was motivated by A Philosophical Approach to MOND, an award-winning book by David Merritt on why it is important for scientific theories to be predictive. While this was common knowledge in the past, this basic aspect of science has been all but forgotten by astronomers thanks to the lack of predictive power inherent to the prevailing cosmological paradigm. To come up with an assessment of whether a theory matches a particular test, I subtracted the theoretical flexibility score from the level of agreement with observations. The results for different tests were then averaged, giving a score for each theory that could in principle be anywhere between –4 and +4.
The idea behind this scoring system is that in an unphysical theory with many free parameters (e.g., the geocentric model), any agreement with observations should generally involve areas where there is a lot of theoretical flexibility. If any strong predictions are made by such a theory, these should typically fail at high significance. There is always the possibility of agreement by pure luck, but this should be very rare. Consequently, we expect very similar scores for theoretical flexibility and the level of agreement with observations. While results for individual tests can differ, we generally expect an unphysical theory to give an average confidence score close to 0 once the results for many tests are averaged. On the other hand, if the physical content of a theory is partly or largely correct, then we expect it to make clear predictions or have unavoidable consequences which are in agreement with observations. In other words, we expect there to be many situations where the model has little theoretical flexibility but still agrees well with observations. We do not expect a positive confidence score in all cases because there could be problems with the observations or other issues, but even so, the average confidence score across many tests should be significantly above zero. In this way, it is possible to assess a theory on its own merits without considering any other theory.
Another important consideration is that some observations are used in the construction of the ΛCDM theory and to set its free parameters. The same applies for MOND. To account for this, I do not consider the test based on the cosmic microwave background (CMB) anisotropies for ΛCDM as their power spectrum is typically used to set the cosmological parameters. The main free parameter in the MOND framework is a0, a fundamental acceleration scale that is sometimes referred to as Milgrom’s constant. a0 was fixed before I was born based on the rotation curves of high surface brightness (HSB) galaxies (Begeman+ 1991). Fortunately, there are a great many lines of astronomical evidence, so the loss of one test for each theory is not a major setback in my attempt to quantify which paradigm better matches the observations.
Table 1: Summary of how well ΛCDM fares when confronted with the data and how much flexibility it had in the fit. The open dot shows that CMB observations were used in theory construction, so this test is not used when assessing ΛCDM. (Table 3 of Banik & Zhao 2022)
My assessment of the ΛCDM paradigm is summarized in Table 1. The test involving the CMB is shown with a hollow dot to indicate that it should not be used to test the model because nowadays the CMB power spectrum is used to fix the free parameters of ΛCDM cosmology. There were referee comments about this and a few of the other tests, which required various changes to the scores. For example, the lithium problem forced a bleaker assessment of how well ΛCDM agrees with the observed primordial light element abundances. Section 10 of my review provides further discussion of the scores assigned to tests where the score was difficult to assign or runs contrary to what people intuitively expect, including also tests where the referee requested alterations to the scores or the splitting of a test into two or more tests. Very few tests of ΛCDM are located towards the top left. Most tests are located close to or even slightly below the line of equality, implying a zero or slightly negative confidence score. As argued above, this suggests an epicycle-like theory where there is some limited validity, e.g. the geocentric model is wrong but it is right about the Moon, which does after all orbit the Earth.
Table 2: Similar to Table 1, but for MOND. The open dot shows that the rotation curves of a handful of HSB galaxies were used to set a0, so these data cannot be used to test MOND. (Table 4 of Banik & Zhao 2022)
Table 2 provides my assessment of how well MOND fares against the considered observational tests. It is sometimes claimed that MOND was designed to fit galaxies, so its successes here do not provide support for MOND. However, a careful reading of the literature reveals that MOND was formulated many decades before the relevant observations became available, with its free parameter fixed more than thirty years ago based on the rotation curves of a handful of HSB galaxies. The many other successes of MOND on galaxy scales are extremely impressive for such an old and inflexible theory. One particularly noteworthy example is low surface brightness (LSB) galaxies, where MOND correctly predicted a large enhancement to the Newtonian gravity of the baryons. Recent work has revealed several important successes of MOND on scales larger than those of individual galaxies. These successes lead to many tests of MOND appearing towards the top left. Importantly, MOND at least plausibly works in all tests considered for my review. There are no areas in strong disagreement with MOND once we consider both theoretical and observational uncertainties.
Table 3: Comparison of ΛCDM (red dots) and MOND (blue dots) with observations based on the tests listed in Tables 1 and 2, respectively. The 2D scores in those tables have been collapsed into a single score for each test. The open dots show tests used in theory construction or to fix free parameters. (Table 5 of Banik & Zhao 2022)
My main goal in this review was to assign a numerical score for how well each theory performs against each test, but in a better way than past such assessments by considering both the agreement with observations and the level of theoretical flexibility. The confidence scores obtained in this way are shown in Table 3. The scores are higher for MOND in nearly all tests on all astrophysical scales. There are a few exceptions, especially on small scales. For instance, General Relativity predicted the observation that gravitational and electromagnetic waves travel at the same speed despite both going through the deep-MOND regions between galaxies. Relativistic extensions of MOND can be made compatible with this constraint, but do not have to be. However, this is only one test. MOND outperforms ΛCDM in the vast majority of tests, especially on the scales of galaxies and galaxy clusters. The addition of a sterile neutrino component is important to MOND elegantly passing the larger scale tests that have been possible so far given the limited work on this area. I argued that a purely baryonic MOND universe is highly unlikely to match the observed properties of galaxy clusters, a fact which has been known for several decades. A hybrid solution is thus required where the dominant mass component of rich galaxy clusters is an undiscovered particle but a known type of particle. In particular, MOND works best if we postulate a fourth type of neutrino with a rest energy of 11 eV (Angus 2009). The average mass density of such neutrinos as a whole would be the same as that of the cold dark matter in the ΛCDM paradigm. This would also explain the acoustic oscillations in the power spectrum of the cosmic microwave background radiation, where MOND differs little from General Relativity due to the strong gravitational fields prior to recombination and a standard expansion history. In the review, I also discussed some very recent evidence that strongly suggests the presence of a sterile neutrino with rest energy of order 1 eV and how this could be consistent with the reported null detections in some experiments.
Table 4: The total confidence in ΛCDM and MOND based on how well each theory performs against each test, bearing in mind its theoretical flexibility (Table 3). The test used to construct each theory is not counted here. The final column shows the average confidence score for each theory across all the tests considered in my review. It is clear that overall, MOND significantly outperforms ΛCDM. (Table 6 of Banik & Zhao 2022)
The average confidence scores for ΛCDM and MOND are listed in Table 4 along with the number of tests used, which is slightly higher in ΛCDM due to it being better developed. The ΛCDM score of 0 is in line with expectations for an unphysical model which may have some right elements and gets some things right by chance. The MOND score of almost +2 indicates plausible agreement in a test with a clear prior prediction. It also corresponds to excellent agreement in a test where we need to make auxiliary assumptions beyond MOND but these only slightly affect the results. I think the score for MOND is about as much as we can expect given the limited funding causing many aspects to be understood after the relevant observations when they could have been predicted a priori with greater investment, the fact that MOND is obviously not a perfect theory, and observational limitations that cause tests with no tension to receive lower observational agreement scores due to measurement errors and astrophysical systematics, e.g. line of sight contamination of galaxy groups. Thus, MOND is strongly favoured over ΛCDM by the huge range of presently available astronomical observations. While some of the data could change in the future, it is almost inconceivable that the 57 point lead of MOND over ΛCDM will ever drop to a negative value such that ΛCDM is favoured over MOND.
Another aspect of the review is that it rebuts many claims to have falsified MOND. I will not go through all of these here, but suffice to say that all these claims were later shown to be erroneous. A common reason is that subsequent observations paint a different picture, e.g. by reducing the velocity dispersion of a galaxy, changing its distance, etc. I encourage readers to check whether a particular paper they are interested in is in the bibliography, and if so, to read what I have said about it in the review. It should already address most of the common objections to MOND, including some very recent ones.
Based on the many diverse lines of evidence considered in the most comprehensive published review of MOND to date, I conclude that ΛCDM is falsified at overwhelming significance by multiple interlocking lines of evidence from a huge range of astrophysical scales, ranging from the kpc scales of galaxy bars to the Gpc scale of the KBC void and Hubble tension. Most if not all of the evidence can be understood in MOND, which in many cases predicted the observations many years if not decades prior to the relevant data becoming available. Making such predictions often took only a very small amount of time and effort due to the ease with which one can do MOND calculations of important observables, e.g. the rotation curve of a galaxy. This stands in stark contrast to the ΛCDM paradigm, where predictive successes are very rare. To paraphrase Laurence J. Peter, “ΛCDM theorists are people who come up with good excuses for why what they predicted yesterday would happen tomorrow failed to happen today.” This has been the situation for many years, with some of the failures now reaching a high level of statistical significance. Therefore, we are at the beginning of a major paradigm shift in astrophysics. In my opinion, the only reasonably analogous situation in the history of science is the heliocentric revolution, since opposition was not so significant in the relativity or quantum revolutions. These are exciting times for astrophysics!
In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.
The Dark Matter Crisis 