LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena

[malawi_glenn]

It is a motivation in arguments that there is any observational support for thinking that there is an observational evidence to motivate BSM physics that Sting Theory could explain, and hence for taking it seriously. I agree that it didn't motivate the initial formulation of the theory.

Do you have any other source where a string theorist lists dark matter particle candidate as a modern motivation?

 

[kodama]

Do you have any other source where a string theorist lists dark matter particle candidate as a modern motivation?

Brian Green and Michio Kaku mention WIMPS and dark matter in their popular books

 

[malawi_glenn]

Brian Green and Michio Kaku mention WIMPS and dark matter in their popular books

I am sure they do, but popular books are ... well ... not a good source of information ...
Let's say I want to fund a string theory research (investigation) group, and I need to write a funding proposal. Should I use those books as a source?

Remember the movie "limitless"? Where the main characters friend /or was it sister...) said he/she read Brian Greenes book in just one day? Why not read GREENs books on Superstring theory? The real deal so to say. I just thought this was a fun anectode.

 

[Davephaelon]

When I first came across Deur's work based on self-interacting gravitons, in analogy with QCD, I was astounded by its elegant simplicity in explaining, for example, the excess orbital velocities of galaxies within a galaxy cluster. Here he invokes flux tubes to account for the additional gravitational attraction between 'point like' galaxies above what would be expected in classical Newtonian gravity. But as evidenced by gravitational lensing a cluster's gravity is enhanced beyond its periphery. It struck me that the extra gravitational potential from the flux tube mechanism would only apply between galaxies but not add to the gravity potential beyond the cluster. It's inconceivable that professor Deur could have overlooked this, so the explanation is probably in one of his papers, which are pretty technical. I'm a bit groggy this morning, but will check later in the morning Ohwilleke's excellent, more layman friendly, write-up on Deur's work to see if I can find something on this.

 

[Davephaelon]

Oops, I see that I already made a query on the issue of explaining enhanced gravity from lensing data beyond the outer boundaries of both galaxies and galaxy clusters, in Deur's SI paradigm, on the thread titled "Do gravitons interact with gravitons". Scanning the responses over there, I see that there is a stackexchange write-up in the last post linked by rcarbajal68 that addresses this issue. I'll give that a lookover.

 

[mitchell porter]

I continue to think it's extremely unlikely that general relativity actually predicts what Deur says it predicts.

More precisely:

@ohwilleke is our best authority on Deur's work. He says (#65 in this thread) that Deur claims these effects occur even in the classical theory. I tried to work out the alleged mechanism in #70.

It must be possible to judge whether this is a reasonable claim, even without exact solutions. Hawking and Penrose proved their singularity theorems by reasoning about geodesics. Surely there's some way to place bounds on what amplified nonlinearity in classical GR can accomplish (perhaps something involving Lyapunov exponents?).

Then there's the quantum version of Deur's arguments. Here the paper I mention in #62 might contain the detailed arguments. Again I am skeptical - yes, gravitons should interact with gravitons, but the interaction ought to be extraordinarily weak, because of the extreme smallness of the gravitational coupling constant. Maybe there's more opportunity for extremely strong nonperturbative effects, e.g. if the gravitational coupling constant runs to large values at small enough scales.

But overall I'm still skeptical here, too. If I ever get around to checking, I might start by investigating whether the approximation of a tensor field (the metric) by a scalar, is messing up the dynamics by introducing an unjustified constraint. (Reducing a tensor to a scalar is a massive truncation of the physical state space, and needs to have a dynamical justification, i.e. there needs to be some cause actively preventing the other degrees of freedom from acquiring forbidden values.)

By the way, what I'm saying is not quite the same as saying that Deur is completely wrong. His calculations could be wrong in general relativity (classical or quantum), but might be right in some other theory of gravity.

 

[ohwilleke]

I continue to think it's extremely unlikely that general relativity actually predicts what Deur says it predicts.

Fair. I certainly don't have the capacity to evaluate that rigorously. There are quite a few papers that he has published in peer reviewed journals and he is a professional full time physicist, so surely this work isn't wildly off the mark. But GR is notorious for being an area where very subtle issues of characterization can make a big difference.

By the way, what I'm saying is not quite the same as saying that Deur is completely wrong. His calculations could be wrong in general relativity (classical or quantum), but might be right in some other theory of gravity.

This is indeed an important point. If you've got gravitational equations that can describe phenomena attributed to dark matter and dark energy over a very great range of applicability, is relativistic in the general sense, can reproduce the CMB and address issues like the impossible early galaxies problem, even if it deviates from Einstein's Field Equations as conventionally applied, then Deur still has a winner, even if he somewhat misunderstands the nature of why his calculations work, and Einstein's Field Equations are probably not quite the right description of reality even though they are really close and excellent in some domains of applicability like strong gravitational fields.

The possibility that the results are really primarily a quantum gravity specific effect are among the possibilities that could make sense.

On the other hand, it is frustrating that there isn't more third-party examination of what is really one of the most promising dark matter particle theory alternatives, to vet it and consider it. The more there are published papers that are not refuted, the more he gets co-authors and publication in peer reviewed articles, and the more that dark matter particle theories and LambdaCDM fall short, the more this work deserves expert attention from GR specialists.

 

[ohwilleke]

There has been plenty of research on nonlinearity in general relativity; there has been plenty of research on stress-energy pseudotensors and partially localized definitions of energy; are there really dramatic new empirical consequences waiting to be revealed, once these two lines of research are considered together?... I also want to understand the relationship between the classical and quantum parts of Deur's research. Hopefully all this can be disentangled with sufficient patience and care.

Another thing that has impeded existing research is that the vast majority of GR papers, in order to make their analytical calculations tractable, assume spherically symmetrical systems, which when present, automatically eliminate the self-interaction effects (which makes sense if conventional wisdom tells you that effects from lack of spherically symmetry aren't important and leading textbooks say so in so many words).

One of the reasons Deur investigated non-sphericially symmetric systems, which GR researchers avoid for convenience in a very large share of work examining how conventional GR as opposed to modifications of it work, is that in QCD (which is his primary specialty in physics) you simply can't do that and get useful results, so he's used to strategies for modeling non-spherically symmetric systems mathematically with which the run of the mill GR researcher is not.

 

[timmdeeg]

This whole discussion doesn't seem to clarify how Deur's gravitational field self-interaction really works.

Apart from this the predictions regarding CMB and Supernovae data are astonishing:

FIG. 2: Power spectrum of the CMB temperature anisotropy FIG. 3: Left panel: Supernova apparent magnitudes vs. redshift.

I wonder if what he calls "the present calculation" shouldn't yield the values of the Hubble "constant" for the early universe und for our local universe too.

Does anyone know if and how Deur's work contributes to resolve the ongoing Hubble-Tension?

 

[ohwilleke]

Does anyone know if and how Deur's work contributes to resolve the ongoing Hubble-Tension?

He hasn't written on the topic yet.

The Hubble constant is not definitionally constant in his work, as phenomena attributed to dark energy in his work are emergent from the emergence of galaxy and large scale structure rather than than being closely related to a cosmological constant term in the equations of GR. So, it might resolve the tension and at a minimum, some sort of tension wouldn't be surprising in his work.

 

[timmdeeg]

He hasn't written on the topic yet.

The Hubble constant is not definitionally constant in his work, as phenomena attributed to dark energy in his work are emergent from the emergence of galaxy and large scale structure rather than than being closely related to a cosmological constant term in the equations of GR. So, it might resolve the tension and at a minimum, some sort of tension wouldn't be surprising in his work.View attachment 315023

http://link.springer.com/content/pdf/10.1140/epjc/s10052-019-7393-0.pdf
Equation (17) yields for present time: 1 = [DM (0)ΩM + DRΩR + DΛΩΛ] − K a2 0 H2 0 , (22)

Sorry I didn't transfer this into Latex.

(17) yields the present time (late universe) Hubble constant expressed by the depletion function$D_M$, whereby $\Omega_R=0$ and $\Omega_{\Lambda}=0$ .

Deur doesn't show a value for $H_0$ explicitly. As he reproduces the supernovae data correctly would this imply the correctness of the late universe Hubble constant, presently around 73 (km/s)/Mpc?

But what if it turns out that the supernovae distance ladder has some systematic failure and thus $H_0$ changes accordingly. Would this eventually support Deur's self-interaction Hypothesis?

 

[ohwilleke]

http://link.springer.com/content/pdf/10.1140/epjc/s10052-019-7393-0.pdf
Equation (17) yields for present time: 1 = [DM (0)ΩM + DRΩR + DΛΩΛ] − K a2 0 H2 0 , (22)

Sorry I didn't transfer this into Latex.

(17) yields the present time (late universe) Hubble constant expressed by the depletion function$D_M$, whereby $\Omega_R=0$ and $\Omega_{\Lambda}=0$ .

Good catch.

Deur doesn't show a value for $H_0$ explicitly. He reproduces the supernovae date correctly. Would this imply the correctness of the late universe Hubble constant, presently around 73 (km/s)/Mpc?

But what if it turns out that the supernovae distance ladder has some systematic failure and thus $H_0$ changes accordingly. Would this eventually support Deur's self-interaction Hypothesis?

It would take a lot more careful analysis and review of that paper for me to tell. Deur's approach does address consistently with the evidence and contrary to LambdaCDM address the impossible early galaxies problem as well as CMB, so it may very well be consistent.

 

[kodama]

He hasn't written on the topic yet.

if dark matter is discovered and explains everything it is said to does that mean Deur is wrong

 

[ohwilleke]

if dark matter is discovered and explains everything it is said to does that mean Deur is wrong

Yes. That would be awesome if it happened. I don't think it will in the next three decades or so.

 

[kodama]

Yes. That would be awesome if it happened. I don't think it will in the next three decades or so.

sterile neutrinos, axions, wimps, even black hole and x17-z'

 

[timmdeeg]

It would proof that Deur's GR field self-interaction mimicking several times the amount of baryonic matter isn't more than a notion but a wrong one.

It seems in GR there is no rigorous calculation instead there is the analogy to QCD whereby Deur refers to a similarity of the Lagrangian. Whereas in QCD the field-interaction exists and is described undoubtedly.

I'm not sure about this: Would field-self-interaction in GR necessarily imply the existence of gravitons?

Is all this the weak point which causes silence in the community?

 

[Davephaelon]

I am greatly impressed by Deur's hypothesis, inasmuch as it conforms to Occam's Razor of minimal assumptions yielding maximum explanatory power. It's remarkable that with gravitational self-interaction alone one can resolve most of the puzzles that have confronted astrophysicists tracing back almost a century. But I say this as one who doesn't have a deep understanding of GR, so I cannot gauge whether his extrapolation of QCD phenomena into the cosmic arena is fully valid. Hopefully, physicists who are specialists in GR will examine his papers and provide us a more rigorous assessment of the plausibility of the ideas expressed in them.

 

[timmdeeg]

if dark matter is discovered and explains everything it is said to does that mean Deur is wrong

Or the other way round. Would dark matter be disproved if astronomers discover that what seems to be dark matter depends on symmetry properties of a matter distribution as predicted by Deur's field self-interaction SI?

... the expectation that GR field selfinteraction effects cancel for spherically symmetric distributions ...

In contrast in flat galaxies SI doesn't cancel mimicking a large amount of dark matter hence.

 

[ohwilleke]

It seems in GR there is no rigorous calculation instead there is the analogy to QCD whereby Deur refers to a similarity of the Lagrangian. Whereas in QCD the field-interaction exists and is described undoubtedly.

There are calculations using a mean-field approximation of classical GR fields and using the GR Lagrangian, in a static approximation (i.e. ignoring particle momentum contributions and electromagnetic flux contributions to the mass-energy tensor on the right hand side of Einstein's equations). QCD motivates the approach taken but isn't actually being used at all to make the calculations.

As a practical matter, it isn't possible to calculate GR effects analytically (i.e. by working out equations rather than doing N-body calculations or some other numerical method) in complex systems like a galaxy.

I'm not sure about this: Would field-self-interaction in GR necessarily imply the existence of gravitons?

No.

Is all this the weak point which causes silence in the community?

Probably not. More likely it is due to (1) the fact that Deur is primarily a QCD physicist publishing outside his primary subfield community in a different subfield of physics (the astronomy of galaxies, GR, and astrophysics), and (2) that non-rigorously derived conventional wisdom in GR is that non-Newtonian GR effects are negligible in galaxy and galaxy cluster scale systems.

 

[ohwilleke]

sterile neutrinos, axions, wimps, even black hole and x17-z'

Narrow sense WIMPs (e.g. supersymmetric WIMPs), and primordial black holes are basically entirely ruled out by existing observations.

Previous experimental hints of sterile neutrinos have likewise been all but ruled out and have found alternative explanations, although neutrino physics researchers continue to look for sterile neutrinos as explanations for new anomalies. Right handed neutrino theories are also exceedingly popular among theorists trying to devise grand unified theories, and among physicists proposing see saw mechanism for neutrino mass.

Any sterile neutrino dark matter candidate has to propose a creation method for them other than thermal freeze out, because something with a sterile neutrino mass suggested by neutrino research would give rise to "hot dark matter" which is inconsistent with the amount of galaxy scale structure observed.

Also, generically, even if sterile neutrinos (or any more massive DM particle) had mean velocities consistent with warm dark matter or cold dark matter, any dark matter particle solution needs to have some kind of self-interaction and/or interaction with ordinary matter sufficient to explain the dark matter halo shapes/distributions that are inferred from astronomy observations. Without that you get NFW halo distributions which are contrary to astronomy observations, and you don't explain the tight link between inferred DM distributions and observed baryonic matter distributions. These problems are generically a problem with a wide array of particle dark matter candidates.

The X17 boson proposed to explain some subtle kinematics of nuclear matter decays interacts too strongly with other matter to be a dark matter candidate.

Likewise, a Z' boson with a different mass than a Z boson, but weak force interactions of a similar magnitude to a Z boson is likewise ruled out by direct DM detection searches, at least in the 1 GeV to 1000 GeV mass range that is usually assumed for a Z' boson, although like any hypothetical particle you can assign pretty much any properties to it to try to fit the data.

Axion-like particle (ALP) dark matter candidate properties are even more ill-defined, and while all are very light there are many, many orders of magnitude of parameter space open. Lots and lots of direct searches from ALP have come up empty, but most of the searches cover only tiny parts of the parameter space. ALPs are also ill motivated in the large part of the parameters space currently being proposed that have nothing to do with the original justification for them to cause the QCD force to have no CP violation.

At some point, ALP DM and effects of gravitons in a quantum gravity regime become hard to distinguish, so the search for ALPs if, in fact, DM effects are really gravitational, may be one of the longest lived DM candidates.

 

[ohwilleke]

This whole discussion doesn't seem to clarify how Deur's gravitational field self-interaction really works.

I have put together an annotated bibliography of the relevant papers along with some prefatory explanations that draw mostly upon one of his power point presentations, to allow anyone who is interested to get a better grasp of these points.

 

[timmdeeg]

I have put together an annotated bibliography of the relevant papers along with some prefatory explanations that draw mostly upon one of his power point presentations, to allow anyone who is interested to get a better grasp of these points.

Very informative, thanks.

 

[kodama]

The X17 boson proposed to explain some subtle kinematics of nuclear matter decays interacts too strongly with other matter to be a dark matter candidate.

High Energy Physics - Experiment​

[Submitted on 29 Sep 2022]

Dark sector studies with the PADME experiment​

A.P. Caricato, M. Martino, I. Oceano, S. Spagnolo, G. Chiodini, F. Bossi, R. De Sangro, C. Di Giulio, D. Domenici, G. Finocchiaro, L.G. Foggetta, M. Garattini, A. Ghigo, P. Gianotti, T. Spadaro, E. Spiriti, C. Taruggi, E. Vilucchi, V. Kozhuharov, S. Ivanov, Sv. Ivanov, R. Simeonov, G. Georgiev, F. Ferrarotto, E. Leonardi, P. Valente, E. Long, G.C. Organtini, G. Piperno, M. Raggi, S. Fiore, P. Branchini, D. Tagnani, V. Capirossi, F. Pinna, A. Frankenthal

The Positron Annihilation to Dark Matter Experiment (PADME) uses the positron beam of the DAΦNE Beam-Test Facility, at the Laboratori Nazionali di Frascati (LNF) to search for a Dark Photon A′. The search technique studies the missing mass spectrum of single-photon final states in e+e−→A′γ annihilation in a positron-on-thin-target experiment. This approach facilitates searches for new particles such as long lived Axion-Like-Particles, protophobic X bosons and Dark Higgs. This talk illustrated the scientific program of the experiment and its first physics results. In particular, the measurement of the cross-section of the SM process e+e−→γγ at s√=21 MeV was shown.

Subjects:	High Energy Physics - Experiment (hep-ex); Instrumentation and Detectors (physics.ins-det)
Cite as:	arXiv:2209.14755 [hep-ex]
	(or arXiv:2209.14755v1 [hep-ex] for this version)
	https://doi.org/10.48550/arXiv.2209.14755

High Energy Physics - Phenomenology​

[Submitted on 19 Sep 2022]

Resonant search for the X17 boson at PADME​

Luc Darmé, Marco Mancini, Enrico Nardi, Mauro Raggi

We discuss the experimental reach of the Frascati PADME experiment in searching for new light bosons via their resonant production in positron annihilation on fixed target atomic electrons. A scan in the mass range around 17 MeV will thoroughly probe the particle physics interpretation of the anomaly observed by the ATOMKI nuclear physics experiment. In particular, for the case of a spin-1 boson, the viable parameter space can be fully covered in a few months of data taking.

Comments:	8 pages, 5 figures and 1 table
Subjects:	High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Experiment (hep-ex)
Cite as:	arXiv:2209.09261 [hep-ph]
	(or arXiv:2209.09261v1 [hep-ph] for this version)
	https://doi.org/10.48550/arXiv.2209.09261

if x17 exist as a spin-1 boson it could be part of a larger dark sector

" In particular, for the case of a spin-1 boson, the viable parameter space can be fully covered in a few months of data taking. "

we'll see possible announced within a year (In particular, for the case of a spin-1 boson)

 

[ohwilleke]

High Energy Physics - Experiment​

[Submitted on 29 Sep 2022]

Dark sector studies with the PADME experiment​

A.P. Caricato, M. Martino, I. Oceano, S. Spagnolo, G. Chiodini, F. Bossi, R. De Sangro, C. Di Giulio, D. Domenici, G. Finocchiaro, L.G. Foggetta, M. Garattini, A. Ghigo, P. Gianotti, T. Spadaro, E. Spiriti, C. Taruggi, E. Vilucchi, V. Kozhuharov, S. Ivanov, Sv. Ivanov, R. Simeonov, G. Georgiev, F. Ferrarotto, E. Leonardi, P. Valente, E. Long, G.C. Organtini, G. Piperno, M. Raggi, S. Fiore, P. Branchini, D. Tagnani, V. Capirossi, F. Pinna, A. Frankenthal

Subjects:	High Energy Physics - Experiment (hep-ex); Instrumentation and Detectors (physics.ins-det)
Cite as:	arXiv:2209.14755 [hep-ex]
	(or arXiv:2209.14755v1 [hep-ex] for this version)
	https://doi.org/10.48550/arXiv.2209.14755

High Energy Physics - Phenomenology​

[Submitted on 19 Sep 2022]

Resonant search for the X17 boson at PADME​

Luc Darmé, Marco Mancini, Enrico Nardi, Mauro Raggi

Comments:	8 pages, 5 figures and 1 table
Subjects:	High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Experiment (hep-ex)
Cite as:	arXiv:2209.09261 [hep-ph]
	(or arXiv:2209.09261v1 [hep-ph] for this version)
	https://doi.org/10.48550/arXiv.2209.09261

if x17 exist as a spin-1 boson it could be part of a larger dark sector

" In particular, for the case of a spin-1 boson, the viable parameter space can be fully covered in a few months of data taking. "

we'll see possible announced within a year (In particular, for the case of a spin-1 boson)

The odds of it not being ruled out are on the order of 0.01%

 

[kodama]

The odds of it not being ruled out are on the order of 0.01%

0.01% is pretty good compare with other BSM physics like EW scale SUSY, LUX dark matter detection, etc.

"the viable parameter space can be fully covered in a few months of data taking. "

0.01% for a chance of one of the biggest mysteries solved with in a year's time

0.01% seems much higher than other BSM HE-physics

the excitement is we should get some evidence for or ruled out within a year's time. i plan to check for updates once a month.

 

[Hornbein]

It seems to me that this question could be answered by examining rotation curves in spherical galaxies. Surely this has been done.

 

[ohwilleke]

It seems to me that this question could be answered by examining rotation curves in spherical galaxies. Surely this has been done.

Few galaxies are totally spherical, but observations have done the next best thing.

Deur has shown rather rigorously that the more spherical a galaxy is the less inferred dark matter content it has:

Observations indicate that the baryonic matter of galaxies is surrounded by vast dark matter halos, which nature remains unknown. This document details the analysis of the results published in MNRAS 438, 2, 1535 (2014) reporting an empirical correlation between the ellipticity of elliptical galaxies and their dark matter content. Large and homogeneous samples of elliptical galaxies for which their dark matter content is inferred were selected using different methods. Possible methodological biases in the dark mass extraction are alleviated by the multiple methods employed. Effects from galaxy peculiarities are minimized by a homogeneity requirement and further suppressed statistically. After forming homogeneous samples (rejection of galaxies with signs of interaction or dependence on their environment, of peculiar elliptical galaxies and of S0-type galaxies) a clear correlation emerges. Such a correlation is either spurious --in which case it signals an ubiquitous systematic bias in elliptical galaxy observations or their analysis-- or genuine --in which case it implies in particular that at equal luminosity, flattened medium-size elliptical galaxies are on average five times heavier than rounder ones, and that the non-baryonic matter content of medium-size round galaxies is small. It would also provides a new testing ground for models of dark matter and galaxy formation.

A. Deur, "A correlation between the dark content of elliptical galaxies and their ellipticity" (October 13, 2020).

Milgrom concluded that elliptical galaxies would have a much lower mass to light ratio than spiral ones back in 1983 with MOND (which is also true), but Deur's finding is more fine grained.

 

[Hornbein]

That seems "highly suggestive."

 

[ohwilleke]

That seems "highly suggestive."

Of course, the thing is that the strong correlation that is observed between galaxy shape and mass to light ratio, which implies in a dark matter particle scenario, the proportion of dark matter and ordinary matter in ay particular galaxy, has no good explanation.

Elliptical galaxies, generally speaking, tend to be larger than spiral galaxies. In a standard galaxy mass assembly scenario in the dark matter particle paradigm, they are formed by the mergers of smaller galaxies. So, they really ought to have all of the DM of their ancestors, rather than than much less.

 

[mitchell porter]

This whole discussion doesn't seem to clarify how Deur's gravitational field self-interaction really works.

In #62, #70, #76, I tried to identify Deur's methods of calculation. And a reminder, Ciotti #44 is the most thorough statement so far, of why one would not expect classical GR to produce such effects. So that's the gap one could try to bridge.

Also, even if that's not how GR works, one could try to design a modified gravity in which Deur's calculations *are* correct.

 

[ohwilleke]

In #62, #70, #76, I tried to identify Deur's methods of calculation. And a reminder, Ciotti #44 is the most thorough statement so far, of why one would not expect classical GR to produce such effects. So that's the gap one could try to bridge.

Also, even if that's not how GR works, one could try to design a modified gravity in which Deur's calculations *are* correct.

One of the things that I'm least clear about is whether Deur's method truly observes both the strong equivalence principle and the weak equivalence principle. I suspect that it observes only one but I'm not sure.

 

[PeterDonis]

QCD motivates the approach taken but isn't actually being used at all to make the calculations.

Even so, the QCD-like effects that Deur appears to be claiming should be much weaker for gravity than for QCD, as compared with the "Newtonian" component of the interaction, because the coupling constant for gravity is so much smaller, and the relative magnitudes of the effects should go like some power of the coupling constant.

 

[PeterDonis]

QCD motivates the approach taken

One major difference between QCD and gravity, though, is that the gauge group of QCD is compact, whereas the gauge group of gravity is not.

 

[kodama]

In #62, #70, #76, I tried to identify Deur's methods of calculation. And a reminder, Ciotti #44 is the most thorough statement so far, of why one would not expect classical GR to produce such effects. So that's the gap one could try to bridge.

Also, even if that's not how GR works, one could try to design a modified gravity in which Deur's calculations *are* correct.

one could try to design a modified gravity in which Deur's calculations *are* correct.--any suggestions for how to go do this ?

 

[kodama]

One major difference between QCD and gravity, though, is that the gauge group of QCD is compact, whereas the gauge group of gravity is not.

could you create a gravity that is like gr but with a compact gauge group