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 [19], lack of observations of Λ-CDM predictions such as the dwarf galaxy problem, or the Hubble tension [20]. 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 [6]-[8], the supernovae observations suggestive of dark energy [10], the tight empirical relation between baryonic and observed accelerations [9, 19], the dynamics of galaxy clusters [6] 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. [10] in the context of the a priori unrelated topic of dark energy.

**Commentary**

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 thatconcludes . . . 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) andsuggests 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).

**Inflation Considered**

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 justinflation, 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).

## 16 comments:

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.

does this imply gravity is asymptomatic safe like qcd

has Stacy McGaugh, ever comment on gravity field self-interaction ?

he told me directly that gravitomagnetism is too weak to be mond

"does this imply gravity is asymptomatic safe like qcd"

Deur has not rigorously evaluated the question. This is, in part, because while his approach is motivated by quantum gravity and by analogy to QCD, in which the outcome is more transparently obvious, it is not an inherently quantum concept and can be applied using plain old classical GR. In Classical GR, the question of asymptotic safety does not arise in the way that it does in quantum theories since classical GR does not involve renormalization.

"has Stacy McGaugh, ever comment on gravity field self-interaction?"

I've mentioned it to him a couple of times and don't recall ever seeing him engage the question one way or the other.

"he told me directly that gravitomagnetism is too weak to be mond"

There is no overlap between Deur's approach and gravitomagnetism. Deur's early works (I haven't fully digested this latest paper) was developed in a static approximation of gravity, while gravitomagnetism is an inherently quantum effect.

Put another way, in Einstein's field equations of GR, the source for the gravitomagnetism arises from a source in the stress-energy tensor on the right hand side of the equations, while the self-interactions of the gravitational field in GR do not.

One reason Deur's analysis hasn't been examined very much in the GR literature before now is that other work has overwhelmingly worked in the spherically symmetric case where the self-interaction effects that Deur is analyzing cancel out, while he is examining effects particular to matter distributions that are not spherically symmetric (informed by what QCD predicts based upon the gravity as QCD squared line of quantum gravity research).

gravity as QCD squared line of quantum gravity research

does this imply that gravity becomes qcd at high energy ?

"does this imply that gravity becomes qcd at high energy?"

No. It merely suggests that quantum gravity ought to behave a lot like the square of the QCD equations. QCD governs the interactions of strong force color charges, while gravity governs the interactions of mass-energy packets, so they wouldn't merge.

The reason for the connection is pretty straightforward.

Gluons interact with each other via the strong force transmitted by massless gluons just as gravitons would interact with each other via the gravitational force transmitted via massless gravitons in a quantum gravity theory. In physics talk both theories are non-Abelian. Also, both QCD and most plausible graviton based quantum gravity theories are "chiral" in the sense that the carrier bosons have helicity (a bosonic analog to parity in fermions), so individual bosons can be left or right handed.

But, gluons are spin-1 bosons (which can be both attractive and repulsive), while gravitons are spin-2 bosons (which are always attractive), which is why you need to use QCD squared, rather than just plain old QCD, as an analog to gravity.

Of course, the analogy isn't perfect. Quarks come in three color charges with exactly the same magnitude, and gluons come in eight color combinations with exactly the same color charge magnitude, while quantum gravity has only one kind of charge (mass-energy with related momentum) that varies basically continuously over a large range of possible values. But the similarities outweigh the differences and QCD physicists are used to doing simulations with different numbers of color charges and quark types as a tool for approximating the physical valued results.

So far, experience has shown that taking a QCD interaction and squaring the equations generally produces the same results as doing an analogous gravitational interaction from first principles, which is great, because QCD, while difficult, is mathematically tractable and can be calculated with, while quantum gravity facially appears to be intractable and not always possible to calculate with in many circumstances because it is not "renormalizable" which is the trick physicists use to avoid infinities in calculations involving the three Standard Model forces. The paradigm leaves hope that perhaps the aspects of quantum gravity that make it impossible to calculate with in the general case can be eliminated through QCD squared methods and that the aspects of quantum gravity that QCD squared doesn't supply may be non-physical artifacts of our mathematically insufficient amplitude calculation methods.

The success of QCD squared methods for understanding quantum gravity calculations also suggests that quantum gravity should have many analogs to QCD phenomena (which are incredibly complex for such a seemingly simple theory).

Electromagnetism is a poor analog to gravity because photons, while being massless, do not themselves interact with each other via the electromagnetic force carried by photons.

The weak force is a poor analog to gravity because W and Z bosons that carry the weak force are not massless, so it is a limited range Yukawa force, and because W bosons interact via the electromagnetic force as well as carrying the weak force.

what If spin - 2 glue balls are massless and stable and infinite range ?

is that gravity ?

Spin-2 glueballs are not massless. In principle, their mass is one of the most straightforward calculations in QCD and they should be 2.4 ± 0.12 GeV/c^2. https://en.wikipedia.org/wiki/Glueball

Even if they were massless (which they aren't, which means that they don't have infinite range), and stable (which they also aren't, as easily determined from QCD calculations), this still wouldn't be gravity as it doesn't couple to mass-energy. Instead, it couples to strong force color charge.

success of QCD squared methods for understanding quantum gravity calculations

might point to some kind of deep relationship, identity even, between QCD and gravity.

perhaps instead of glueballs gravity is the residual vander waals type interaction of QCD.

if you can find a physical interpretation of qcd squared, perhaps that is also gravity?

btw does Deur ever derive in a rigorous fashion mond scale of acceleration ao and explain why it is on the same order as the cc?

"if you can find a physical interpretation of qcd squared, perhaps that is also gravity?"

Definitely not. The similarity can be explained entirely from having massless self-interacting carrier bosons. This line of thinking is a total dead end.

Erik Verlinde has worked on a SM force derivation of gravity, called "emergent gravity", but it doesn't proceed an a QCD squared mode of analysis. Instead, he "describes gravity as an emergent phenomenon that springs from the quantum entanglement of small bits of spacetime information. As such, entropic gravity is said to abide by the second law of thermodynamics under which the entropy of a physical system tends to increase over time." Also, while it is emergent, it doesn't actually have fewer degrees of freedom than general relativity. It simply treats the Planck length as fundamental, and Newton's constant as derived, instead of the other way around. See generally https://en.wikipedia.org/wiki/Entropic_gravity

"btw does Deur ever derive in a rigorous fashion mond scale of acceleration ao"

No.

In principle, it should be possible to derive it from first principles using Newton's constant.

But, he uses the observationally determined MOND constant a0 to set the value of the constant "a" appearing before the self-interaction term in the General Relativity Lagrangian, rather than calculating it from first principles. He does so basically by adjusting it so that it reflects the residual that is left over after integer, pi, and Newton's constant factors which arise naturally in deriving the Lagrangian are considered.

"and explain why it is on the same order as the cc?"

In Deur's analysis, GR doesn't have a cosmological constant and it isn't actually a constant (there are some figures illustrating this in the main paper blogged in this post), nor is Hubble's constant.

Instead, the enhancement of gravity within galaxies and galaxy clusters leads to an equivalent diminishment of gravity between galaxies and galaxy clusters. It is this diminishment of gravity between galaxies and galaxy clusters gives rise to what is perceived as the cosmological constant and/or dark energy. This is why the aggregate apparent dark energy in lambda CDM is of the same order of magnitude as the dark matter content of lambda CDM. This is also why the apparent cosmological constant is on the same order of magnitude as a0.

In judging Deur's work, there's two questions to ask:

Does the kind of self-interaction he wants, actually follow from the quantization of general relativity?

and

Would that kind of self-interaction, actually explain the astronomical and cosmological observations?

For now my main interest is the first question. I would like to understand how Deur's ansatz looks from the perspective of "mainstream quantum gravity", e.g. perhaps John Donoghue's effective field theory of perturbative quantum gravity. Or just how it looks to someone who has seriously studied quantum gravity, like Haelfix at Physics Forums.

The mainstream perspective on quantizing general relativity, is that you end up with an infinite number of interaction terms (involving arbitrary numbers of gravitons interacting at a point), each of which has an undetermined coefficient. The infinity of terms is what they mean by nonrenormalizable - such a theory would require an infinite number of measurements in order to establish those parameters. But in practice, if you restrict yourself to low energies, you can neglect all but a finite number of terms (assuming that the higher terms don't have unnaturally large coefficients), and this is the basis of Donoghue's gravitational EFT.

So one question would be, can Deur's approach be interpreted as a thesis about the coefficients in the Donoghue effective theory, or does it involve concepts outside that framework?

The fact that no one else has ever commented on the theoretical basis of his work, suggests that he's doing something deeply unorthodox - but what? Maybe you could ask about it at Stack Exchange.

(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).Do you hypothesize a cyclic universe model with two universes (one matter dominated and one antimatter dominated) expanding and contracting in each cycle?

Also, what are your thoughts on the new cyclic universe model of Paul Steinhardt and Anna Ijjas with smooth and non-singular (no crunch and hence no cosmic singularity) bounces and with no involvement of string theory, higher dimensions and branes (and probably compatible with modified gravity theories and Deur's theory)?

https://www.youtube.com/watch?v=S7-HNi2ne44

https://www.youtube.com/watch?v=c2gOZ_xVQII

https://www.youtube.com/watch?v=KHhqZfsI0Hs

https://www.youtube.com/watch?v=mvoxOLMU5Z4

https://arxiv.org/abs/1904.08022v1

https://bouncingcosmology.com/

And finally, what are your thoughts on Roger Penrose's cyclic universe model (which you probably already know well)?

@Onur

My strong intuition is that there is not a cyclic or bouncing universe. Just a single universe that expands both forward and backward in time from the Big Bang and never reverses itself.

I think that inflation theory is probably a result of bad Bayesian priors and bad modeling of how the universe evolves over time, but I don't entirely rule it out.

I don't watch videos.

@Andrew

Thanks for the answer.

So you think spacetime began roughly 13.8 billion years ago for both the matter dominated universe and the anti-matter dominated universe and there was nothing before that.

Both Paul Steinhardt's new cyclic universe model and Roger Penrose's cyclic model rule out inflation. Though both cyclic models wait for verification or refutation.

Luckily for you, the arxiv.org paper I linked to explains all the major points of Paul Steinhardt's new cyclic model, so you do not have to watch all those videos. Also, his bouncingcosmology.com website I linked to includes the rest of his papers on his new cyclic model, I would suggest you read only the most recent ones (since about 2014), the earlier ones relate to his earlier cyclic model he no longer maintains.

@Andrew

As a sequel to my last comment, I should add that the commonly hypothesized Big Bang is a singularity and as such an anomaly for physics. So even if you do not accept any of the cyclic universe models, you still need to provide an alternative explanation to the commonly hypothesized Big Bang in order to counter the physically impossible and nonsensical singularity explanation. Saying the universe began about 13.8 billion years ago does not do away with the singularity. You could simply say you do not know what happened in the early fractions of a second after the hypothesized moment of Big Bang, ascribing a beginning and age to the universe/spacetime does not resolve the singularity problem. And if there was no beginning of the universe/spacetime about 13.8 billion years ago or at any other time in the past and it has always existed in some form (thereby resolving the singularity problem), then some kind of cyclic model could be one of the likeliest models for the universe/spacetime.

@Onur It is, of course, unknowable at this point and highly speculative.

One way to describe anti-matter is as regular matter moving backward in time.

In that interpretation you get a dynamical Big Bang that isn't necessarily an entirely uncrossable barrier, nor a perfect singularity, and get matter-antimatter annihilation as the dynamo of the Big Bang.

@Andrew

So you posit that the universe/spacetime began about 13.8 billion years ago with the Big Bang but that the Big Bang was not a singularity. How exactly do you resolve the singularity problem?

Also, unlike most Big Bang hypotheses, your Big Bang does not show only white hole characteristics, but both white hole and black hole characteristics depending on the time and kind of matter in question.

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