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.

68. A critical essay by Subir Sarkar on the standard model of cosmology

(Guest post by Nick Samaras, April 12th, 2022)

Nick Samaras is a Ph.D. student at the Astronomical Institute of Charles University, in the Faculty of Mathematics and Physics, in Prague, Czech Republic. He works on cosmological simulations with Milgromian Dynamics (MOND). He has obtained his M.Sc. degree in Theoretical Physics at Cergy University, in France after having completed his B.Sc. in Mathematics at the Aristotle University of Thessaloniki, in Greece. In his following guest post he writes about the cosmological principle and a recent essay titled “Heart of Darkness” by Prof. Subir Sarkar.

The Standard Model of Cosmology (SMoC) has been considered as the correct description of the Universe and its evolution for decades now. General Relativity along with the mysterious Dark Energy, embedded on the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, provide the outset for the ΛCDM (Λ Cold Dark Matter cosmological) model. The FLRW metric is a formula derived from the General Relativity and corresponds to a homogeneous, isotropic and expanding universe. It is the mathematical tool with which one calculates distances on a 4-dimensional (time and the 3 dimensions of space) model. Nonetheless, according to more sophisticated investigations and the increase of observational data, the current theory faces a great number of challenges.

The Homogeneity and Isotropy hypothesis holds a convenient ground to do Cosmology. The so-called Cosmological Principle states that the Universe is very much alike anywhere over a typical scale of about 250/h Megaparsec (Mpc) (1 parsec = 1 pc is approximately equal to 3.26 light-years, unit of length). Remember that the Milky Way has a diameter of approximately 40 kpc, the Local Group of Galaxies is about 3 Mpc across, and the Virgo supercluster spans over about 30 Mpc). However, do the observations agree with this? Is there enough evidence to install the Cosmological Principle on a solid paradigm? How concrete are the cornerstones of the SMoC?

Subir Sarkar, an Emeritus Professor at the Rudolf Peierls Centre for Theoretical Physics, University of Oxford, argues that the real universe to be very different to the ΛCDM model and in particular the Cosmological Principle to be violated. Unraveling the record, the cosmological constant Λ (often being referred to as Einstein’s biggest blunder, the cosmological parameter causing the accelerating expansion) differs by many orders of magnitude when estimated from Quantum Field Theory (QFT), compared to what is inferred from Cosmology. He also emphasises an inconsistency when attempting to calculate the vacuum energy in QFT. The fact that the zero-point (vacuum) energy does not gravitate (otherwise it would have already dominated the Universe letting it evolve in a completely different way) have been kept aside even by the great Wolfgang Pauli, Prof. Sarkar points out.

Besides “the worst theoretical prediction in the history of physics” (Michael Hobson, George Efstathiou, and Anthony Lasenby), looking at the Cosmic Microwave Background (CMB – the primordial relic radiation released approximately 300,000 years after the Big Bang), its anisotropy dipole is larger than expected at high redshift (a cosmological way to calculate distances from us, based on the redshift of spectral lines). He notes that all matter in our nearby Universe has a coherent bulk flow approximately aligned with the direction of the CMB dipole. Several experiments, spanning from the 70s until these days, show that the bulk flow continues out to approximately 300 Mpc, remarkably not converging to homogeneity. The Indian theoretical astrophysicist wonders about Milne’s quote “the Universe must appear the same to all observers”, advocating historical changes in the field.

Sakar and his collaborators identified that the large dipole is not from the local universe. They have discovered that the cosmic rest frame of matter traced by quasars and the CMB don’t coincide. Thus, it is determined that the apparent acceleration is not happening because of the cosmological constant. It’s only a result of our non-Copernican position in the bulk flow. Consequently, the cosmic acceleration is not isotropic. ΛCDM begins to disintegrate …

Dark Energy, which drives the cosmos to accelerated expansion, in the form of an until-now-completely-not-understood repulsive force increasing with time, is therefore an occurrence generated by an over-interpreted conventionalised model which needs to be seriously revised. Leaving out the inflationary era a few moments after the Big Bang and the ambiguous premise of Dark Matter, the SMoC has been tested sufficiently to be replaced by a more detailed developed theory. Last, Prof. Sarkar, supporting that the Universe has different matter contents in different regions, encourages younger researchers to work out in greater depth an improved model of the real Universe .

Find here the essay “Heart of Darkness” by Prof. Subir Sarkar.


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.

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.

55. “A Philosophical Approach to MOND” wins prestigious award

It is with delight we learned today that David Merritt’s book on “A Philosophical Approach to MOND” published by Cambridge University Press won the Prose Award for Excellence in Physical Sciences and Mathematics. Other authors also competing for this price were Peebles and Weinberg. 

I had written a review of this book which can be read here.

Note also that in 2013 David published a noteworthy text book on “Dynamics and Evolution of Galactic Nuclei” (with Princeton Series in Astrophysics).


This is an opportunity to recall how I personally stumbled into this whole problem concerning dark matter (see also this article on Aeon): My research up until the mid1990s was based on stellar populations, although in Heidelberg we had also measured, for the first time, the actual space velocity of the Magellanic Clouds (in 1994 and 1997). These were my first endeavours into the extragalactic arena. I had heard a fabulous lecture by Simon White who was visiting Heidelberg, showing movies of structure formation in the LCDM model they had just computed in Garching. I personally congratulated Simon for this most impressive achievement.  One could see how major galaxies were orbited by many dwarf satellite galaxies and how all of that formed as the Universe evolved. I had also noted from photographs that when two gas-rich galaxies interact, they expel tidal arms in which new dwarf galaxies form. These new dwarf galaxies are referred to as tidal dwarf galaxies.

The Tadpole Galaxy recorded with the Hubble Space Telescope’s Advanced Camera for Surveys. Evident are the new dwarf galaxies in the 100 kpc long tidal tail.

In the 1990’s the community had largely discarded satellite dwarf galaxies being tidal dwarfs because it was known that they cannot have dark matter (this goes back to Barnes & Hernquist,1992,  later confirmed by Wetzstein, Naab & Burkert 2007).  So it was thought that tidal dwarfs just dissolve and play no important role.  The observed satellite galaxies of the Milky Way have large dynamical M/L ratios, going up to 1000 or more. This proved they can contain a 1000 times more mass in dark matter than in stars and gas. So obviously they cannot be tidal dwarfs. I very clearly remember Donald Lynden-Bell exclaiming in Cambridge, when I was still visiting regularly, that his suggestion that the satellites came from a broken-up galaxy cannot thus be correct, since they contain dark matter. Then I made my discovery (truly by pure chance) published in Kroupa (1997), which made me think that what the celebrated experts are telling me seemed not to be quite right. After this publication I was told more than once this work made me un-hireable.
 
I had then noted (Kroupa et al. 2005), that the disk of satellites (DoS, including the newer once which Donald had not known) is in conflict with them being dark-matter substructures, as these ought to be spheroidally distributed around the Milky Way galaxy. 
 
We  argued (to my knowledge for the first time in print, in Kroupa et al. 2010 and in Kroupa 2012 ) that the disk of satellites can only be understood if they are tidal dwarfs. I had also come to the conclusion that my chance discovery above is unlikely to be able to explain the high M/L values of all the satellite galaxies as they would all need to be quite strongly affected by tidal forces which poses a problem for those further than 100 kpc from the Milky Way because their orbital periods begin to approach a Hubble time. And if they are tidal dwarfs (which they must be given they make a disk of satellites),  then this implies we need non-dark-matter models, i.e. , we need to change the law of gravitation to account for the high M/L values these little galaxies display.  Subsequently I was quite fevering (with PhD student Manuel Metz and later Marcel Pawlowski) each time a new satellite was discovered to see where it lay (I used to run to their offices whenever some survey reported a new satellite), and ultimately what the proper motions are doing: if the satellite galaxies form a pronounced disk of satellites then they must be orbiting only within this disk (Pawlowski & Kroupa 2013). I was (this was already in the 2000s) also interested if  John Moffat’s “modified gravity” (MOG) might explain the large M/L ratios, and John Moffat visited me in Bonn. But it turns out that MOG is falsified while Milgromian gravitation (MOND) is, as far as one can tell, the at the moment only possible gravitational theory we can use which accounts for all data and tests so far performed.  Oliver Mueller, Marcel Pawlowski  et al. (2021) affirm that the Milky Way is not unique in having a disk of satellites system. Observing disks of satellites around larger galaxies is not a “look elsewhere effect” since the very-nearest large galaxies are looked at, rather than finding such DoSs around some host galaxy in a very large ensemble of observed galaxies. I think the disk-of-satellites or satellite-plane problem is the clearest-cut evidence why we do not have dark matter. 
 
The (negative) test for the existence of dark matter particles (warm, cold, fuzzy) via Chandrasekhar dynamical friction is the other (Kroupa 2015).
 
Plus, with all the other tests performed in strong collaboration with Indranil Banik (notably Haslbauer et al.  2019a, Haslbauer et al. 2019b,  Haslbauer et al. 2020 and Asencio et al. 2021) it materialises that the tests all lead to mutually highly consistent results – we do not have the situation that one test is positive (for dark matter), the other not. They all turn out to be consistently negative. Indranil Banik concludes correctly (Feb.5th, 2021): “There are so many lines of evidence that no single one is critical any more.”
 
I am personally deeply impressed how everything seems to fall into place (quite nearly everything) once one uses MOND (which is based on a Lagrangian etc.).  Apart from completely naturally resolving the Hubble Tension and easily accounting for massive high-redshift galaxy clusters like El Gordo (see also this account on Triton Station), the DoSs or satellite planes form naturally (as shown independently by Banik et al. 2018 and by Bilek et al. 2018) and these tidal tail dwarf galaxies have large M/L values due to the correct law of gravitation (e.g. this amazing prediction by McGaugh 2016 of the velocities of stars in one of the satellite galaxies and verification thereof by Caldwell et al. 2017).
 
But, just like with the standard model of particle physics, there definitely is a deeper layer to MOND which we have not yet discovered; a more fundamental theory, which may well be the quantum vacuum which also explains particle masses. Milgrom had already published seminally on this issue.
 
The huge success of MOND comes not only in it naturally account for the data on scales of a few 100 pc to a Gpc, but also that it is a “progressive research programme“, with the standard dark-matter based models being “degenerative“.  For details, see David Merritt’s book above. 
 

In The Dark Matter Crisis by 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.