We check whether General Relativity's field self-interaction alleviates the need for dark matter to explain the universe's large structure formation. We found that self-interaction accelerates sufficiently the growth of structures so that they can reach their presently observed density. No free parameters, dark components or modifications of the known laws of nature were required. This result adds to the other natural explanations provided by the same approach to the, inter alia, flat rotation curves of galaxies, supernovae observations suggestive of dark energy, and dynamics of galaxy clusters, thereby reinforcing its credibility as an alternative to the dark universe model.
The consistency of the standard Λ-CDM model of the universe in explaining many observations that would be otherwise problematic is a compelling argument for the existence of dark matter and dark energy.
Yet, there are good reasons for studying alternatives to Λ-CDM, e.g. the lack of detection of dark particles, the dwindling support from theories beyond the standard model of particle physics, observations that challenge the dark matter model such as , lack of observations of Λ-CDM predictions such as the dwarf galaxy problem, or the Hubble tension . The credibility of an alternative approach is enhanced if, like for Λ-CDM, it can consistently explain the otherwise puzzling cosmological observations.
One alternative approach proposes that these observations are explained by the self-interaction of gravitational fields in General Relativity. It naturally explains the galactic rotation curves -, the supernovae observations suggestive of dark energy , the tight empirical relation between baryonic and observed accelerations [9, 19], the dynamics of galaxy clusters  and the Tully-Fisher relation [6, 10, 16].
The explanation is natural in the sense that a similar phenomenology is well-known in the context of QCD, a fundamental force whose Lagrangian has the same structure as that of General Relativity. Crucially, no free parameters are necessary, nor exotic matter or fields, nor modifications of the known laws of nature.
In this article, we checked whether the approach also explains the formation of large structures. We found that field self-interaction strengthens sufficiently the gravitational force so that the small CMB inhomogeneities can grow to the density presently observed.
Again, no free parameters were needed: the function that globally quantifies the effect of field self-interaction had been previously determined in Ref.  in the context of the a priori unrelated topic of dark energy.
Deur's work is, in my humble opinion, by far the most plausible and credible explanation of the phenomena attributed to "dark matter" and "dark energy", and the most promising foundation from which to develop a theory of quantum gravity. Dark matter is the only phenomena known for which there seems to be overwhelming evidence that core theory (i.e. the Standard Model plus General Relativity as conventionally applied) definitely can't explain. The mass of the Higgs boson, first observed in 2012, for example, is at a value that would allow the Standard Model to produce sensible predictions all of the way up to Big Bang energies.
Multiple factors distinguish Deur's approach from all of the dark matter, dark energy, and modified gravity alternatives - strictly speaking his approach isn't any of these things.
In Deur's view, "dark matter" and "dark energy" are simply the product of disregarding gravitational field self-interactions in weak gravitational fields in favor of Newtonian gravitational approximations of General Relativity in complex galaxy scale and larger systems, something that has been done rather thoughtlessly and without much rigorous analysis, when it is inappropriate to do so and overlooks important observable consequences of the non-linear part of General Relativity in non-spherically symmetric, galaxy scale or larger systems.
Deur reproduces the successes of MOND, while curing its phenomenological defects in galaxy clusters and other relativistic circumstances.
Deur provides an exact equation for MOND effects in particular types of galaxies, rather than an empirically fit toy model approximation, and provides a theoretical basis for MOND behavior derived from a theory of gravity that has already worked extraordinarily well for more than a century in the face of myriad strong field observational tests.
Deur does all of this with just one, universal, experimentally measured parameter, in addition to Newton's constant. But this constant is determinable, in principle, from first principles (although he hasn't actually done the first principles derivation of it). Meanwhile, Deur removes one of the experimentally measured physical constants, the cosmological constant, from the ranks of fundamental constants in the "core theory" of the Standard Model plus General Relativity, thereby improving on the status quo.
Thus, Deur manages to fit all of the observation data to which his approach has been applied, with no free parameters or equation terms not already fixed by General Relativity a century ago. In contrast, the best dark matter particle theory simulations require sixteen finely tuned free parameters to match what we observe.
Deur reduces the amount of mass-energy in the universe attributed to the dark sector by about 95%, with lambda CDM currently estimating that the universe is about 68% dark energy and 27% dark matter, although the potential systemic error in the dark energy energy component is greatly overestimated. This could also help solve the "flatness problem."
Deur's work eliminates the theoretical motivation to find primordial black holes, a search that has so far come up completely empty, not identifying even one of them, although a few small corners of parameter space remain to rule them out as a dark matter candidates or as actual phenomena at all.
Deur's cosmology can explain everything we observe entirely with Standard Model fundamental particles, with one exception, which isn't strictly speaking necessarily required. He calls for only one particle beyond the Standard Model, and then, only if it is expressed as a quantum gravity theory. This is the absolutely plain vanilla massless spin-2 graviton that couples to particles in proportion to their mass-energy with a strength expressed by Newton's constant, which every quantum gravity researcher predicts. But he doesn't even require that General Relativity be formulated as a quantum gravity theory to achieve his results.
Deur solves the profound conservation of mass-energy problem of general relativity with a cosmological constant, or alternative dark energy theories, in an elegant way that no one else that I am aware of has seriously even attempted. This may be the only possible solution to observed dark energy phenomena that does so. Everyone else has simply been content to make one exception to the conservation of mass-energy, or to look for systemic error in estimating it. He actually solves this problem.
Like the universe of modified gravity theories generally, Deur's approach lacks the many serious flaws of the various dark matter particle theories that seem to be growing in number every few months.
In Deur's approach, the non-detection of dark matter particles is expected. The close correlation between baryonic matter content and apparent dark matter now flows directly from a formula, with the deviations from the scaling relations observed attributable to the geometry of the mass distributions. The tendency of satellite galaxies to fall in a plane with spiral galaxies is explained. The enhanced attraction of wide binary stars is explained. The apparent lack of dark matter suggested by 21cm data is explained. The impossible early galaxy problem is resolved, while still producing correct levels of large scale structure in recent times. The behavior of galaxy cluster collisions like the Bullet Cluster is no longer problematic (it currently is a problem in both dark matter particle theories where it is too improbable, and in some, but not all, modified gravity theories).
While he hasn't done it yet, Deur's approach should almost surely be able to reproduce the Cosmic Microwave Background radiation spectrum that a phenomenologically extremely similar relativistic MOND theory has already been able to reproduce.
Deur's approach explains why inferred dark matter halos do not fit the NFW distribution that they should in lambdaCDM theory. Deur's approach explains the "cosmic coincidence" issue.
Eighteen years have passed since Deur's first preprint on this approach was published in September of 2003. He has published nine peer reviewed scientific journal articles on the topic since then, two with co-authors, and has another that looks likely to be published that has co-authors. Essentially no one else has cited his work, or built upon it, but it is also true that in all that time, not a single published article or pre-print comment has poked a hole in his analysis.
In contrast, many other attempts by outsiders to the sub-field of astrophysics to explain dark matter phenomena with General Relativity, or to explain dark energy phenomena with General Relativity without a cosmological constant, such as a recent attempt to explain spiral galaxy rotation curves with gravitomagnetic effects in galaxies, have been quickly shot down.
Two of Deur's most recent articles have reached his conclusions from ordinary classical General Relativity, rather than from the quantum gravity enhancement of General Relativity that originally motivated his analysis, which makes the claims he has made in his papers less extraordinary at a theoretical level, even though his approach completely upsets the modern cosmology paradigm.
The resistance of the scientific establishment to Deur's work is understandable. Deur's primary professional experience and training is as a QCD physicist, not a astrophysicist or cosmologist.
Distinguished general relativity scholars have stated that General Relativity shouldn't matter in these systems (without doing sufficiently rigorous analysis to confirm this without loopholes for non-spherically symmetric systems) and that gravitational self-interactions shouldn't be important, to the point that established researchers in astrophysics assumed this was a dead end that didn't bear serious investigation.
If Deur is right, every single dark matter particle theorist and major collaborations like the Planck collaboration have been fundamentally barking up the wrong tree pursuing what amounts epicycles, and even the modified gravity theorists have been somewhat wrong in believing that gravity had to be modified when it was right all along but misapplied.
Essentially every astronomy and cosmology observation in the last half century that was previously interpreted in terms of the leading lambdaCDM theory of cosmology, or the cosmological constant, or another dark matter particle theory, or an incorrect modified gravity theory, has to be revisited and reinterpreted. And, the analysis of the very complex system of the universe using Deur's approach, as this most recent paper illustrates, is a lot more subtle and tricky to conduct analytically, than the analysis using conventional lambdaCDM theory.
General Relativity without a cosmological constant is also significantly easier to formula as a quantum gravity theory than General Relativity with a cosmological constant.
The End Of Fundamental Physics?
Without unexplained phenomena to describe, theoretical work proposing dark matter candidates and modifications to gravity, and support for experimental searches for them would fade to a slight simmer.
Dark matter candidates are also the strongest observational motivation for particle physics searches for beyond the Standard Model fundamental particles, and that motivation would disappear as well.
Deur's work isn't the only reason for theorists proposing wild new beyond the Standard Model particles or forces, which have been spewing out in arXiv preprints in a steady flow for years, to be disheartened, however.
After more than a decade of operation, the Large Hadron Collider still hasn't found any meaningful hints of new fundamental particles or forces other than the long predicted Standard Model Higgs boson, despite exploring energy scales much higher than any previous experiment.
Lepton universality violations are the only serious anomalies that remain outstanding at this point and for reasons that I have expressed in previous posts, I think it is likely that these are due to look elsewhere effects, to unrecognized systemic error, or to incorrectly modeled theoretical predictions (with this last option being most likely).
Furthermore, I noted in an April 7, 2021 blog post, reporting the latest muon g-2 measurement:
[A] Lattice QCD collaboration known as BMW released a new paper in Nature that concludes . . . that the leading order hadron vacuum polarization calculation which is the dominant source of theoretical error in the Standard Model prediction should be calculated in a different matter that it turns out is consistent to within 1.6 sigma of the combined muon g-2 measurement (and to within 1.1 sigma of the Fermilab measurement) and suggests that the Standard Model is complete and requires no new physics. Meanwhile another preprint announced an improved calculation of the hadronic light by light contribution to the Standard Model prediction that also moves the prediction closer to the experimental value[.]
Another theoretical group using different methods came up with a different prediction for the value of muon g-2 that is in significant tension with the new Fermilab measurement. But, I personally have almost no doubt that the BMW calculation and the other improved calculation announced the same day, are the correct ones. This leaves very little room for new physics at energy scales that can be experimentally probed in the foreseeable future.
Most consequentially, these developments, taken together, essentially put nails in the coffin of supersymmetry theories and with them, string theory, which needs to have a supersymmetry theory as its low energy effective theory. Scientists looked long and hard in all the right places for evidence of supersymmetry and came up empty handed. This dominant paradigm in the theoretical physics community is breathing its dying gasps.
Deur's work, and the latest muon g-2 and LHC results, leave "core theory" reigning supreme. It may take another generation for theorists to stop proposing new physics that these developments leave us without a need to explain with new physics. But the writing is already on the wall.
This doesn't entirely leave physicists chasing the ultimate fundamentals with nothing to do (and, of course, there are plenty of non-fundamental physics questions like those raised by condensed matter physics, fluid dynamics, hadron physics, nuclear physics, and the star, planet and galaxy formation process, that are left to answer).
But these developments should refocus the fundamental physics sub-discipline seeking the ultimately complete laws of Nature on: (1) the source of the fundamental constants in the Standard Model which seem to have a pattern to them (which I suspect involves an extension of Koide's rule and the LP&C relationship in the context of electroweak unification theory as key elements), (2) on hammering out the details of neutrino physics (and especially the mechanism by which neutrinos acquire their mass which I strongly suspect is not Majorana in nature), (3) on figuring out what is behind apparent observations of lepton universality violations (which I suspect will disappear with further analysis and experimental work), and (4) on matter creation (i.e. baryogenesis and leptogenesis) which is a matter that I also think has a relatively straightforward explanation that isn't really contrary to Standard Model physics or General Relativity (i.e. an anti-matter dominated universe expanding outward in the opposite direction in time from our universe that is a counterpart to our own post-Big Bang universe).
Pretty much the only gravitational element of modern cosmology upon Deur's approach remains agnostic is cosmological inflation (which isn't a consensus view even now, in cosmology and comes in hundreds of different flavors, at least dozens of which are still potentially consistent with observations).
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from 10−36 seconds after the conjectured Big Bang singularity to some time between 10−33 and 10−32 seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago). . . .
It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe. Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed.
Deur's current paper traces cosmology from 370,000 years or so after the Big Bang known as "recombination time", while inflation pertains only to a first fraction of a second after the Big Bang, so it isn't obvious if Deur's approach would change the analysis to date. But, as this paper shows, it does already greatly move back the time frame at which dark energy phenomena begin to emerge and become relevant to about 1 billion years after the Big Bang, which is much earlier than in the current paradigm.
I wouldn't be surprised, however, if once the dust settled and all existing data was reinterpreted in light of Deur's work, that cosmological inflation turns out to be unnecessary to explain our observations (although this is merely my own rank conjecture).