75. No trace of dark matter in the dwarf galaxies of the Fornax Cluster

(by Pavel Kroupa and Elena Asencio) 

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.

Press releases about this publication:

in German from Bonn University,

in English: from the University of Bonn and from the University of St. Andrews,

in Czech from Charles University in Prague.

This post is related to the previous DMC Blog 58.

Talks about this project are available (the criticisms raised in the discussion of the ESO talk have been accounted for in our publication Elena Asencio, Indranil Banik et al. 2022, MNRAS, in press).

Elena explains the results in St. Andrews:

And at ESO (critical questions were raised at 34 minutes into the video – see below):

Jumped to 34m:


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

73. A composition for iai: Dark matter doesn’t exist! Yearly, a three quarter billion USDollars are wasted on an illusion.

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:

Dark matter doesnt exist

A straight pdf version for download is available here:

For a version in Spanish see “Einstein estaba equivocado: necesitamos una nueva teoría del cosmos“. A critique appeared as “Kroupa on Dark Matter vs MOND“.

Related to the above iai publication is the piece that appeared on Nov.25th, 2016, in aeon: “Has dogma derailed the scientific search for dark matter?“. Presentations are available on YouTube: Heidelberg Colloquium (November 2013), “The Vast Polar Structures around the Milky Way and Andromeda“, Golden Webinar (April 2021), “On the Non-Existence of Dark Matter“, and Astronomy on Tap Koeln (March 2022), “Dark Matter Kindergarten Stuff“. In May, 2021, Sabine Hossenfelder explained “Dark Matter, The Situation has Changed“.

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.

71. From galaxy bars to the Hubble tension: a comprehensive review of evidence concerning MOND

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).

Since 2012, the dark-matter-based cosmological models are thus ruled out as viable theories for the Universe with more than 5sigma confidence. This is also discussed independently by Bjorn Ekeberg in “The Breakdown of Cosmology” and David Merritt’s “A Philosophical Approach to MOND”.

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.

70. The List of Flawed Falsification Claims about MOND

Modern theories in physics need to be tested and, if they significantly fail a test, discarded. Significant means a prediction that is different from the measurement many times the uncertainty. For example, a calculation in a theory A predicts the space ship to end up at a point which is five million km away from where the astronauts are meant to be, and if the uncertainty is only 100km, then we need to reconsider if this theory A might not pose a threat to the lives of the astronauts. A calculation in theory B might, on the other hand, place the astronauts on target (say only 50km away) and they live. Clearly, theory B is preferred over theory A.

In this sense, the dark-matter based theories (case A above) have been rigorously and robustly falsified to any high degree of standard in the physical sciences (see previous and next post). What about MOND (theory B above)? It too is a physical theory allowing predictions. It too can be ruled out.

Srikanth Togere Nagesh has put a large effort to track down and document the published falsifications of MOND. It turns out that the claimed falsifications of MOND have all been shown, in the published scientific research literature via rebuttals, to be flawed. In every case either wrong calculations were done or some essential physical process that acts within MOND and normal matter has been wrongly applied or even ignored. This is touched upon in the Addendum to post 69, and here we publish the full list of tests of MOND that claim MOND is out. As found by Srikanth, all are erroneous and have published rebuttals:

Why do so many researchers publish such sub-standard results? This is probably a sociological issue: a researcher benefits in the eyes of the “ΛCDM priests” if the researcher shows MOND to be wrong. The “ΛCDM priests” disfavour MOND, because if MOND is the valid approximation to the physical Universe, then the dark-matter based models are invalid. This would put “ΛCDM priests” out of job. A researcher who hopes (i) to get a prize, (ii) to publish in Nature, (iii) to get a raise in salary, (iv) to rise up in the career ladder, will thus like to publish anti-MOND results, and would often get away with it, if there were not brighter scientists who still upkeep the ideals and standards of research in the natural sciences.

Cases in point are the incorrect claims that MOND is ruled out published in Nature and Nature Astronomy (see items 17 and 18 and in The List of MOND-falsification claims).

Doing the work needed to write a rebuttal is costly, and so the here documented largely sub-standard “MOND-falsification” research is pulling down the entire research effort. The bright researchers cannot spend as much of their valuable time on actually advancing our understanding of nature, because they are constantly paralysed by needing to react to some new MOND-falsification claim. While it is necessary to keep testing MOND, this needs to be done at high quality.


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

65. The Don’t-Look-Up Syndrome of Cosmology: Chicago Cosmologists at their best; and the Hubble Tension does not exist

(by Pavel Kroupa, Friday 21st January 2022)

We humans are, as any living creature, and by necessity, conservative beings. We need to be, since typically most of us prefer to sustain their comfortable arrangements. The cave person will prefer to stay near their cave if the nearby plains below are full of fodder, and they would kill off threats. The cosmologist prefers to stay with their dark matter that made them big and important. So when a comet/climate crisis is discovered to approach Earth and is calculated, with some margin or uncertainty, that it will extinguish known life, it can be easier for the majority to just ignore this and to trust in everything turning out all right in the end. Keep the high spirits up, don’t worry and keep smiling and do not frown, do not spoil the mood by doomsday blubber, don’t look up to the threat. So let us ignore that the temperature of the oceans has already increased by nearly 2 degrees centigrade and that another increase by three will kill off most plankton as shown by Sekerci & Petrovskii (2018) with Earth’s atmosphere consequently running out of oxygen.

What has this to do with modern cosmology? I would claim: everything. The modern, successful homo cosmologicus vehemently defends their dark matter against all odds, even if it means killing the scientific method (testing and falsification of hypotheses using reproducible logical methods); they resist change to their habitat as long as the vast landscape of rewards, awards, grants and riches remains abundant.

On Friday, January 14th, 2022, I watched the Golden Webinar on the Hubble Tension, and on this same Friday there appeared on the arXiv an Annual Review on cosmology. Both scientists (speaker and author) are from the highbrow Kavli Institute for Cosmological Physics at the University of Chicago, and both contributions I found to be remarkable.

In the Golden Webinar on “Tension in the Hubble Constant – Does it mean new Physics?“, the speaker very nicely explained the measurements of the Hubble constant using different distance ladders and which role the uncertainties play. Three points struck me: (1) The speaker declared that the physical reason for the Hubble Tension remains unknown. (2) The speaker declared there to be no other known major tension between observations and the Standard Model of Cosmology (the SMoC, or LCDM model). (3) During the panel discussion, a long time was spent on Penrose’s Conformal Cyclic Cosmology hypothesis and it was speculated that fading dark matter might account for the Hubble Tension. The panel largely agreed that no one knew what dark matter was – it might have a large number of degrees of freedom, thus allowing the introduction of an arbitrary number of free parameters to fit almost anything.

Concerning the three points above, I wrote into the chat two questions (see Figure 1 below). Essentially, accepting the well-observed Gpc-scale KBC void as being a real structure of the Universe, the Hubble Tension must then arise from it logically (Haslbauer et al. 2020). This is because galaxies are accelerated gravitationally towards the sides of the void, and an observer within the void (as we are) then measures an apparent faster expansion of the local Universe (see figure 2 in 52. Solving both crisis in cosmology: the KBC-void and the Hubble-Tension). The Hubble Tension therefore has a very simple physical explanation.

In fact, a real Hubble Tension does not exist: it is merely an apparent effect caused by the observed KBC void (Haslbauer et al. 2020), and it would have been predicted if Wong, Suyu et al. (2020) and Riess et al. (2021) had not made their observations of expansion. It is the same reason, in essence, why apples fall to the Earth: replace the galaxies by apples, and they will fall to where they are attracted to, which is the side of the underdensity.

It was a wonderfull event and fascinating to see how the panel very happily discussed the entirely speculative fading dark matter concept in the context of the Hubble Tension, but no-one appeared to dare to raise the possibility that it might simply be due to the observed KBC void, as in fact it must be. I tried to help the panel by posting my question into the chat, but it appeared to me that, in the intimidating presence of highbrow scientists, discussing fading dark matter was acceptable, while raising the obvious solution was no-go. After all, who wants to ask a seemingly silly down-to-Earth question (“can the observed Gpc underdensity be responsible for the apparent Hubble Tension?”) in view of such intellectual Mt. Everests.

The second point above by the speaker I also found impressive, given that other independent falsifications of the LCDM model at more than five sigma confidence have been published, see the list A-F below. It seems that these contributions were missed in Chicago, or that Chicago Cosmologists “do not look up”. I guess they do not need to look up, since they are already on Mt. Everest.

I am still trying to digest this, which is why I wrote the above first paragraph.

Figure 1: My chat contribution. It received 7 votes, the highest of all questions, but the panel did not raise this issue with the speaker.

Why was neither the Golden Webinar speaker nor the panel willing to delve into the true physical reason for the Hubble Tension? I think that the problem is that the KBC void, which causes the Hubble Tension, falsifies the SMoC with more than 5sigma confidence (Haslbauer et al. 2020), because the SMoC cannot grow such large and deep under densities within a Hubble time. And furthermore, the Chicago Cosmologists, as represented by the speaker and author (next), seem adamantly to refuse to discuss MOND seriously. But MOND is the only known modern non-relativistic theory of gravitation in which the Universe can grow such a large observed void and observed early very massive interacting galaxy clusters (Asencio et al. 2021). We covered this galaxy-cluster problem on a previous occasion. In MOND, there is no Hubble tension (since the voids form naturally) and very massive interacting galaxy clusters also form naturally in the earlier Universe.

On the same day as the above Webinar, an Annual Review on “The Road to Precision Cosmology” was published on the arXiv: It is to appear in Ann.Rev.Nucl.Part.Sci. 72:1-33, https://arxiv.org/abs/2201.04741v1 .

I was interested, since the author is viewed by many to be an outstanding cosmologist, and I expected a fair, balanced and up-to-date review of cosmology for the community of Nuclear and Particle Physicists. This is an important review: Annual Reviews are corner stones of literature. Often they are the first entry point into a research field. Their role is thus truly important. On contemplating the review, I decided to write the following letter – let it speak for itself:

Letter sent on 17th of January 2022 to those addressed (with minute modifications for this forum):

Dear author,

(CC to Editors, Committee Members and Staff of the Annual Review of Nuclear and Particle Physics, and researchers working on MOND),

Concerning your review article "The Road to Precision Cosmology" which is to appear in Ann.Rev.Nucl.Part.Sci. 72:1-33,     https://arxiv.org/abs/2201.04741v1 :

I kindly ask you to adjust this article to represent the modern state of affairs truthfully: As it stands, the article is not a review but a biased misrepresentation of the state-of-the art in the research field. It misrepresents the entire field of cosmology to the research community in Nuclear and Particle Physics. 

If not-citing highly relevant research literature is considered to be equivalent to plagiarism, then you have provided a major example of such ill conduct: "Papers published in A&A should cite previously published papers that are directly relevant to the results being presented. Improper attribution — i.e., the deliberate refusal to cite prior, corroborating, or contradicting results — represents an ethical breach comparable to plagiarism." (citing from "Ethical issues: the A&A policy concerning plagiarism and improper attribution: https://www.aanda.org/index.php?option=com_content&view=article&id=136#Ethical_issues ).

In your article, we read "Sec. 3.1.2. False starts. In 1983, Milgrom noticed...."

This is an unacceptable representation of an entire highly successful and vibrant research field in which an increasing number of brilliant young physicists are active in.  You claim in this section that MOND cannot be falsified. This is wrong. We are actively working on falsifying this theory. MOND can be falsified by, for example, finding systems that do not obey the non-linear MOND Poisson equation.

Your article is not aware of or purposefully ignores that 

  1. The LCDM standard model of cosmology is in tension with the data on many different scales with significantly more than 5 sigma confidence.
  2. The data which are in tension with LCDM are at the same time naturally (i.e. without adjustment of any parameter) explained in a cosmological model which is based on Milgromian gravitation (MOND) without cold or warm dark matter.

Some of the relevant very recent major peer-reviewed research contributions (ignored by your article) on this are:

A) The existence of LCDM dark matter particles is in more than 5sigma tension with observed bar pattern speeds through the test based on Chandrasekhar dynamical friction published in 2021: Fast galaxy bars continue to challenge standard cosmology.

B) Very massive galaxy clusters form and interact at high redshift being in more than 5sigma tension with LCDM published in 2021: A massive blow for ΛCDM - the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology.

C) The observed local Gpc scale underdensity causes the Hubble tension and is in more than 5sigma tension with LCDM published in 2020: The KBC void and Hubble tension contradict ΛCDM on a Gpc scale - Milgromian dynamics as a possible solution,

Apart from the above extreme inconsistencies of the LCDM model with the respective data (spanning kpc to Gpc scales), MOND accounts for these naturally and it also naturally accounts for:

D) A planar group of galaxies recedes too rapidly from the Local Group (in >3.96 sigma tension with LCDM) published in 2021: On the absence of backsplash analogues to NGC 3109 in the ΛCDM framework.

E) The lack of a bar in the nearby disk galaxy M33 could not be explained in LCDM published in 2020: The Global Stability of M33 in MOND.

F) The planar (disk-like) distribution of satellite galaxies is inconsistent with LCDM but arises naturally in MOND published in 2018: MOND simulation suggests an origin for some peculiarities in the Local Group and Origin of the Local Group satellite planes.

Your article neither cites nor discusses these, and falsely implies the LCDM model to be consistent with the data at the precision level. Further, the review appears to suggest there to be no other model (without dark matter) that can claim comparable success. Claiming today that the LCDM model is a "triumph of precision cosmology" (Sec. 4.1 in your article) is purposefully propagating outdated misinterpretations to an audience who are non-experts in this research field. 

I will publish the contents of this email as an open letter, and I hope to receive a constructive reaction. 


Sincerely,

Pavel Kroupa

(Helmholtz-Institut for Nuclear and Radiation Physics, Bonn;                        Astronomy Institute, Charles University, Prague)


The interested reader might also consult “It’s time for some plane speaking” published by Marcel Pawlowski (2021) in Nature Astronomy. Although Marcel suggests there to be no obvious solution in sight, in MOND, the solution is quite trivial. The planes of satellites come from galaxy-galaxy encounters, as explicitly demonstrated by Bilek et al. (2018, A&A and 2021, Galaxies) and Banik et al. (2018, MNRAS).


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

61. The crisis in the dark matter problem becomes a historically unparalleled failure in the scientific method

This year, Pavel Kroupa was asked to hold a Golden Webinar in Astrophysics on the dark matter problem. This contribution provides the link to the recording of this presentation which has now become available on YouTube. In this presentation, Pavel Kroupa argues that the dark matter problem has developed to become the greatest crisis in the history of science, ever. This contribution also provides links to recordings available on YouTube of previous related talks by the same speaker from 2010 (the Dark Matter Debate with Simon White in Bonn) and 2013 (in Heidelberg). This might allow some insight into how the debate and the research field have developed over the past dozen or more years.

1) Golden Webinar: “From Belief to Realism and Beauty: Given the Non-Existence of Dark Matter, how do I navigate amongst the Stars and between Galaxies?”

On April 9th, 2021, Prof. Pavel Kroupa presented a talk in the Golden Webinars in Astrophysics series on “From Belief to Realism and Beauty: Given the Non-Existence of Dark Matter, how do I navigate amongst the Stars and between Galaxies?”. The talk is now available on Youtube:

The slides to the talk without the fictitious story can be downloaded here:

If you are interested in other talks presented during The Golden Webinars in Astrophysics series, you can find the record of those already presented on their Youtube Channel, and here is a list of upcoming talks. The Golden Webinars are provided as a free public service and have no registration fees.

2) The vast polar structures around the Milky Way and Andromeda

In November 2013, Prof. Pavel Kroupa presented “The vast polar structures around the Milky Way and Andromeda” in the Heidelberg Joint Astronomical Colloquium. In the talk he discussed the failures of the Standard model of cosmology and the implications for fundamental physics.

A blog entry from 2012 on the vast polar structure (VPOS) of satellite objects around the Milky Way can be found here.

3) Bethe-Kolloquium “Dark Matter: A Debate”

In November 2010, Prof. Simon White (Max Planck Institute of Astrophysics, Garching) and Prof. Pavel Kroupa (University of Bonn) debated on the concept and existence of dark matter during the Bethe Colloquium in Bonn. Their presentations and the subsequent debate are available here:

a) Presentations by Prof. White and Prof. Kroupa

Summary of both presentations:

b) The Debate

The German-language television channel 3sat produced a TV report on the Bethe Colloquium, which can be also found on Youtube (available only in German):

Part I

Part II


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

60. Recent review talks about MOND, the Hubble tension and MOND cosmology including major problems of the dark matter models to match data

1) To obtain an introduction to MOND and MOND-cosmology, those interested might like to watch the talk below by Dr. Indranil Banik (past AvH Fellow in the SPODYR group at Bonn University, now at St.Andrews University). It was held on Sept. 30th, 2021 at the University of Southampton.

Indranil Banik

https://m.youtube.com/watch?v=jL09gRe1q7s

Also, the following two previous talks are relevant:

2) In the recent Newton 1665 physics seminar series on  “MOND, the KBC void and the Hubble tension” by Dr. Indranil Banik and Moritz Haslbauer (SPODYR group):

Moritz Haslbauer

3) And also recently, as a CosmoStat Journal Club seminar on “El Gordo: a massive blow to LCDM cosmology” by Dr. Indranil Banik and Elena Asencio (SPODYR group): 

Elena Asencio


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

58. The tidal stability of Fornax cluster dwarf galaxies in Newtonian and Milgromian dynamics

(Guest post by Indranil Banik and Elena Asencio, August 2nd, 2021)

A directly-related presentation by Elena Asencio is available here:

The tidal stability of Fornax cluster dwarf galaxies in Newtonian and Milgromian gravity

The slides of the presentation can be downloaded here:

A large number of dwarf galaxies in the Fornax cluster (Figure 1) appear to be disturbed, most likely due to tides from the cluster gravity. In the standard cosmological model (ΛCDM) , the observable structure of the dwarfs is barely susceptible to gravitational effects of the cluster environment, as the dwarfs are surrounded by a dark matter halo. Because of this, it is very hard to explain the observations of the perturbed Fornax dwarfs in this theory. However, these observations can be easily explained in MOND, where dwarfs are much more susceptible to tides due to their lack of protective dark matter halos and the fact that they become quasi-Newtonian as they approach the cluster center due to the external field effect.

Figure 1: Fornax galaxy cluster. The yellow crosses mark all the objects identified in the Fornax deep survey (FDS) for this region of the sky, the black circles are masks for the spikes and reflection haloes, and the red crosses mark the objects that pass the selection criteria to be included in the FDS catalog. Image taken from Venhola et al. 2018.

The impact of tides on what the dwarfs look like is illustrated in Figure 2, which shows the fraction of disturbed galaxies as a function of tidal susceptibility η in ΛCDM and MOND, with η = 1 being the theoretical limit above which the dwarf would be unstable to cluster tides. Moreover, there is a lack of diffuse galaxies (large size and low mass) towards the cluster center. This is illustrated in Figure 3, which shows how at low projected separation from the cluster center, dwarfs of any given mass cannot be too large, but larger sizes are allowed further away. Figure 3 thus shows a clear tidal edge that cannot be explained by selection effects, since the survey detection limit would be a horizontal line at 1 on this plot such that dwarfs above it cannot be detected. Diffuse dwarf galaxies are clearly detectable, but are missing close to the cluster center. Another crucial detail in Figure 3 is that dwarfs close to the tidal edge are much more likely to appear disturbed, which is better quantified in Figure 2 in the rising fraction of disturbed galaxies with tidal stability η. The tidal edge is also evident in Figure 2 in that the dwarfs only go up to some maximum value of η, which should be close to the theoretical stability limit of 1. This is roughly correct in MOND, but not in ΛCDM.

Figure 2: Fraction of disturbed galaxies for each tidal susceptibility bin in MOND (red) and ΛCDM (blue). Larger error bars in a bin indicate that it has fewer dwarfs. The bin width of the tidal susceptibility η is 0.5 in MOND and 0.1 in ΛCDM (each data point is plotted at the center of the bin). Notice the rising trend and the maximum η that arises in each theory.

Figure 3: Projected distances of Fornax dwarfs to the cluster center against the ratio Re/rmax, where Re is the dwarf radius containing half of its total stellar mass, and rmax is the maximum Re at fixed stellar mass above which the dwarf would not be detectable given the survey sensitivity. The dwarfs are classified as “disturbed” (red) “undisturbed” (blue). The black dashed line shows a clear tidal edge – at any given mass, large (diffuse) dwarfs are present only far from the cluster center. This is not a selection effect, as the survey limit is a horizontal line at 1 (though e.g. some nights could be particularly clear and allow us to discover a dwarf slightly above this).

We therefore conclude that MOND and its corresponding cosmological model νHDM (see blog post “Solving both crises in cosmology: the KBC-void and the Hubble-Tension” by Moritz Haslbauer) is capable of explaining not only the appearance of dwarf galaxies in the Fornax cluster, but also other ΛCDM problems related to clusters such as the early formation of El Gordo, a massive pair of interacting galaxy clusters. νHDM also better addresses larger scale problems such as the Hubble tension and the large local supervoid (KBC void) that probably causes it by means of enhanced structure formation in the non-local universe. These larger scale successes build on the long-standing success of MOND with galaxy rotation curves (“Hypothesis testing with gas rich galaxies”). MOND also offers a natural explanation for the Local Group satellite planes as tidal dwarf galaxies (“Modified gravity in plane sight”), and has achieved many other successes too numerous to list here (see other posts). Given all these results, the MOND framework appears better suited than the current cosmological model (ΛCDM) to solve the new astrophysical challenges that keep arising with the increase and improvement of the available astronomical data, which far surpass what was known in 1983 when MOND was first proposed.


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

56. From Belief to Realism and Beauty: Given the Non-Existence of Dark Matter, how do I navigate amongst the Stars and between Galaxies?

(by Pavel Kroupa, 4th of April, 2021, 11:11)

Update (April 15th): After receiving some queries, the slides to the talk w/o the fictitious story can be downloaded here

On April 9th, 2021, I will give this public talk:

If interested, you can join the public lecture by registering here.

The talk, held via zoom, is on April 9that 11:00 Chilean Time (CLT = UTC-4),  8am Pacific Daylight Time (PDT = UTC-7),11am Eastern Daylight Time (EDT = UTC-4), 17:00 Central European Summer Time (CEST = UTC+2)

The Golden Webinars are provided as a free public service and have no registration fees. They are recorded and made available for later viewing via youtube.


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

54. The interacting galaxy cluster “El Gordo”: a massive blow to ΛCDM cosmology

(Guest post by Elena Asencio, University of Bonn, January 16th, 2021)
 
It is currently accepted that structure in the Universe formed in a hierarchical way. In other words, smaller structures formed first and then merged into larger structures. The largest gravitationally bound structures in the Universe are the galaxy clusters. Since the predicted timescale in which these structures formed depends on the cosmological model adopted and, subsequently, on the gravity theory assumed, galaxy clusters can be used to test both gravity theories and cosmological models models on large scales.
 
In the last decades, the improvements in telescope detection capabilities have made possible to observe objects which are deeper in space. The further an astronomical object is from us, the longer it takes for its light to reach us. Therefore, deeper surveys allow us to observe how the Universe looked like in the fairly distant past. Some of the galaxy clusters that were detected in these deep surveys surpass the standard model (ΛCDM) predictions in terms of mass, size and/or galaxy-infall velocities, and could potentially pose a serious problem to the model.
 
El Gordo (ACT-CL J0102-4915) is a galaxy cluster with particularly extreme properties. It is located more than 7 billion light years from Earth and is composed of two sub-clusters weighing together approximately 3e15 Solar masses with a mass ratio of 3.6 and a high collision velocity of approximately 2500 km/s. Due to the highly energetic interaction of its two sub-clusters, it is also the hottest and most X-ray luminous galaxy cluster observed at this distance according to Menanteau et al. (2012).
 

Figure 1: A composite image showing El Gordo in X-ray light from NASA’s Chandra X-ray Observatory in blue, along with optical data from the European Southern Observatory’s Very Large Telescope (VLT) in red, green, and blue, and infrared emission from the NASA’s Spitzer Space Telescope in red and orange. Notice the twin tails towards the upper right.Image from this source. Credits: X-ray: NASA/CXC/Rutgers/J. Hughes et al; Optical: ESO/VLT & SOAR/Rutgers/F. Menanteau; IR: NASA/JPL/Rutgers/F. Menanteau.

 
In our paper “A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology” (Elena Asencio, Indranil Banik & Pavel Kroupa 2021), we conducted a rigorous analysis on how likely it is that this object exists according to ΛCDM cosmology.
 
In order to do this, we searched for cluster pairs that could potentially be progenitors of the El Gordo cluster in the ΛCDM cosmological simulation developed by the Juropa Hubble Volume Simulation Project  – also known as the Jubilee simulation. The reason why we searched for the El Gordo progenitors instead of directly looking for an El Gordo-like object is because extremely large objects like El Gordo require very large simulation boxes to have their number of analogues estimated in a reliable way. Larger simulation boxes have lower resolution. Therefore, when searching for El Gordo analogues in the simulation, we can not aim to match its morphological properties (e.g. the observed X-ray morphology) — as these would need a high resolution simulation with gas dynamics to be reproduced. Such simulations covering a sufficiently large volume cannot be achieved today even on the most powerful supercomputers (and are in actuality also not necessary for the present aim) — but we can try to find cluster pairs whose configuration matches the initial configuration of El Gordo in terms of total mass, mass ratio and infall velocity. To determine the values of the parameters describing this initial configuration, we need to rely on the results of detailed hydrodynamical simulations. Zhang et al. (2015) performed a series of hydrodynamical simulations of two colliding galaxy clusters trying to find which set of initial conditions would result in a merger with similar properties to El Gordo. Among the 123 simulations that they ran for different parameters, they found that the model that gave the best fit to the observed properties of El Gordo had a total mass of 3.2e15 Solar masses, a mass ratio of 3.6, an infall velocity of 2500 km/s, and an impact parameter of 800 kpc. Models with lower mass or lower infall velocity were not able to reproduce the twin-tailed morphology of El Gordo (see Figure 1) and its high X-ray luminosity.
 
Using the Jubilee simulation, we found no analogues to El Gordo. We therefore relaxed the requirement of a sufficiently high mass, and found out how the number of El Gordo analogues (in terms of mass ratio and infall velocity) decreased with increasing mass. Since the Jubilee simulation was run for different cosmological epochs or redshifts, we were also able to determine how the number of El Gordo analogues (in terms of total mass, mass ratio, and infall velocity) decreased for earlier epochs or larger redshift. From these results and accounting for the fact that the total volume of the Jubilee simulation is significantly larger than the space volume in which El Gordo was found, we obtained the probability of finding a cluster pair with a similar configuration to the expected pre-merger configuration of El Gordo, at a slightly earlier epoch to that at which we observe El Gordo (see Figure 2).
 

Figure 2: Plot showing the frequency of analogues to the El Gordo progenitors for each position in the grid. The grid is constructed for a series of mass values in log10 scale (y-axis) and cosmic scale factor a (x-axis). The a values determine the cosmological epoch (for reference, a = 1 today, a = 0.535 at the epoch at which we observe El Gordo and a = 0.5 at the epoch at which we look for El Gordo progenitors, and generally the expansion factor a and redshift z are related by a=1/(1+z) ). The probability of lying outside a contour (region of fixed colour) can be expressed in terms of the number of standard deviations (σ). The higher the number of standard deviations at a certain point in the grid, the further away will this point be from the expected value of the distribution. It is generally considered that if a model surpasses the 5σ threshold, then this model is falsified. In this plot, the point in the grid corresponding to the and a values of the El Gordo progenitors is marked with a red X and it corresponds to 6.16σ. In terms of probability, this is equivalent to saying that there is a 7.51e-10 chance of finding an interacting pair of El Gordo progenitors or an even more extreme pair in the ΛCDM model.

 
 
The chance of observing an El Gordo-like object in the ΛCDM cosmology is 7.51e-10, which corresponds to 6.16σ (as a reminder: physicists accepted the existence of the Higgs boson once the experimental data reached a 5σ significance level — in general, when a phenomenon reaches a confidence of 5σ or more, then it is formally taken to be certain corresponding to a chance of one in 1.7 million that the phenomenon is untrue). This means that, assuming the ΛCDM model, we should not be observing El Gordo in the sky (but we do observe it). In fact, the tension between the ΛCDM model and the observations is even higher if one takes into account that El Gordo is not the only problematic object found in the sky.
 
Another well-known galaxy cluster that poses a potential problem to ΛCDM is the Bullet Cluster. It is also an interacting cluster composed of two subclusters colliding at high velocity (3000 km/s) which, according to the ΛCDM model, is unexpected at the distance at which it is observed (3.72 billion light-years).
Kraljic & Sarkar (2015) obtained a 10% probability of finding a Bullet Cluster analogue in the ΛCDM cosmology over the whole sky. In order to get a more helpful estimate of the Bullet Cluster probability, the sky area in which the Bullet Cluster was observed should be taken into account – it would not be realistic to use the probability for the whole sky as this would imply that the Bullet Cluster was found in a fully sky survey, which is not the case. Taking into consideration that the survey in which the Bullet Cluster was found only covered 5.4% of the sky, the actual probability of observing a Bullet Cluster-like object is 0.54%, which makes it a 2.78σ outlier. Combining the probability of observing both the Bullet Cluster and El Gordo in the sky raises the tension to 6.43σ.
 
We also considered the possibility that the problem is not in the ΛCDM model but in the Jubilee cosmological simulation, in the Zhang et al. (2015) hydrodynamical simulations, or in our statistical analysis. According to Watson et al. (2014), up to now, the Jubilee simulation has been shown to work correctly in accordance with the ΛCDM cosmological model for which it was designed. So we have no reasons to believe that there might be any problems with the Jubilee simulation in that regard. We also found many lower mass analogues to El Gordo, so numerically our results should be quite sound and allow an accurate extrapolation up to the El Gordo mass. The results of Zhang et al. (2015) for the initial configuration of El Gordo are backed up by previous independent studies of El Gordo. The weak lensing analysis of El Gordo by Jee et al. (2014) confirms the mass estimate of 3e15 Solar masses. The simulations by Donnert (2014) and Molnar & Broadhurst (2015) agree on an infall velocity of 2250 – 2600 km/s. Besides this, Zhang et al. (2015) had already checked that lower values for the mass and infall velocity – which would be easier to explain in ΛCDM – were unable to reproduce the morphology of El Gordo. Regarding our own analysis, in the paper we also performed the statistical analysis with a different method to check the consistency of our results. The results were indeed consistent, so we consider our methods to be reliable. The more conservative and detailed method is shown in Figure 2.
 
Since the ΛCDM model cannot account for the existence of extreme objects like El Gordo or the Bullet Cluster, some authors tested other cosmological models to check how well they work in this respect. Katz et al. (2013) searched for El Gordo analogues in a simulation that adopted a νHDM cosmological model. The νHDM model has the standard hot Big Bang, primordial nucleosynthesis, CMB and expansion history as the ΛCDM model, but assumes the extended gravity law devised by Milgrom (MOND) and the presence of an undetected mass in galaxy clusters composed of particles like sterile neutrinos that only interact with gravity (see the post “Solving both crises in cosmology: the KBC-void and the Hubble-Tension” by Moritz Haslbauer for a more detailed explanation of the νHDM model). Using this model, Katz et al. found that about one El Gordo analogue was expected to be encountered in their simulation box, while they could not find any analogues when they performed a simulation of similar characteristics with the ΛCDM model. Accounting for the fact that the volume of the survey in which El Gordo was found is slightly different from the volume of the simulation used by Katz et al. (2013), we determined that the number of El Gordo analogues that we expect to observe in a νHDM model is 1.16. Therefore, the vHDM model gets the right order of magnitude for the frequency of El Gordo-like objects. The reason for this is that the growth of structure is enhanced in MONDian gravity, so it is more natural to find very massive objects like El Gordo at high redshift in models that assume this type of gravity.
 
But then, if smaller structures formed first and larger structures formed afterwards, how is it possible that we do not observe more super-massive objects like El Gordo at closer distances? The fact that structures form more efficiently in MONDian gravity also implies that larger and deeper voids will be generated with this gravity law. This prediction is in agreement with the results of Keenan, Barger & Cowie (2013), who observationally found that the local Universe is immersed in an underdensity bubble (the KBC void) with a radius of about one billion light years. For this reason, it is not expected that very massive objects will be able to form in the nearby regions of our Universe, as these regions will have a low density with respect to the mean density of the global Universe (see the post “Solving both crises in cosmology: the KBC-void and the Hubble-Tension” by Moritz Haslbauer for a more detailed explanation of the KBC void). Therefore, the νHDM model is capable of explaining the presence of super-massive objects like El Gordo at distant epochs and is also able to explain the absence of objects like this in the local Universe.
 
We conclude that El Gordo falsifies ΛCDM at 6.16σ (6.43σ if we take into account the Bullet Cluster too). We propose the νHDM cosmological model as a possible explanation to the formation of extreme objects like El Gordo or the Bullet Cluster at very early cosmological epochs. Moreover, the νHDM model also explains other observations that cannot be justified with the ΛCDM model, such as the existence of the KBC void, therewith automatically resolving the Hubble tension and accounting for the lack of super-massive galaxy clusters like El Gordo in the local Universe. Since the νHDM cosmological model automatically accounts for  the observed stellar dynamics in the smallest dwarf and most massive galaxies, the rotating-planar distributions of satellite galaxies, and many other observed properties of galaxies and large scale structure, it is clear that it poses a far superior framework than the (in any case falsified) ΛCDM model for understanding the Universe.
 

In The Dark Matter Crisis by Elena Asencio. A listing of contents of all contributions is available here.