One should keep in mind that most dark matter "alternatives", including this one, actually include dark matter. It says so right on the 2nd page of their paper:
> Consider requirement (iii), that is, successful cosmology. In (2) we have a new d.o.f. φ [...] What should the expectation for a cosmological evolution of ϕ be? The MOND law for galaxies is silent regarding this matter. There is, however, another empirical law which concerns cosmology: the existence of sizable amounts of energy density scaling precisely as a^(−3).
In other words, they are saying that to get the cosmology right, they need to add stuff that behaves exactly like dark matter -- that is what they are alluding to with the "sizable amounts of energy". They make their φ field play this role. It's just like TeVeS, the other major relativistic MOND theory, where the scalar "S" field does the same thing.
The popular press likes to frame the debate as "dark matter vs. modified gravity", but it's really "dark matter vs. dark matter plus modified gravity", which is much less dramatic.
is that right? You're referring to the fact that in general in modern physics a "field" implies a field-carrier particle. Lambda-CDM dark matter theories specifically posit that various astronomical discrepencies can be explained using particles that only interact gravitationally, with a huge number of degrees of freedom (e.g. the difference between the bullet cluster and the milky way alone represents a LARGE set of degrees of freedom).
This seems rather different from a "single" field which may have a particle (that may or may not itself interact gravitationally), with only one additional degree of freedom.
> The popular press likes to frame the debate as "dark matter vs. modified gravity", but it's really "dark matter vs. dark matter plus modified gravity", which is much less dramatic.
Honestly for us lay folks there isn't a perceptible difference in the amount of drama between the two. :)
> We remark that A_\mu also contains a pure vector mode perturbation which is expected to behave similarly as in the Einstein-Æther theory [90, 91]"
Their [91] is Jacobson & Mattingly https://arxiv.org/abs/gr-qc/0007031 whose §VII (DISCUSSION) contains this, which I struggle to see as helpful for them: "With the action adopted in this paper the aether vector generically develops gradient singularities even when the metric is perfectly regular. We take this as a sign that the theory is unphysical as an effective theory". (That doesn't stop Jacobson from investigating things like (time-independent) black hole solutions https://arxiv.org/abs/gr-qc/0604088 "It is a plausible conjecture that nonsingular spherically symmetric initial data will evolve to one of the regular black holes whose existence has been demonstrated here, but this has certainly not been shown", and worse they show that the aether does not obey the Raychaudhri equation, so the relativistic MOND authors seem to need more ghosts).
And given how hard it has been to find the "Dark Matter", theories that reduce the amount of it seem like valuable contributions to the overall understanding. Dark matter has so many "if its like ... then ..." scenarios that theories like this are effectively "working backwards" on the problem by giving us better constraints on the "then ... " part.
> Unlike dark matter models that are often based on fundamental symmetry principles—the new model was not conceived with an underlying theory in mind. However, such a theoretical basis might be uncovered using the new MOND model.
I think this is an important thing to keep in mind. Cosmology has a big challenge right now. There is something fundamental in the universe that we don't understand. While dark matter is currently our best explanation, it is deeply flawed; it predicts the existence of an entire class of matter that we've been unable to find any physical proof for other than cosmology (and cosmology is the thing we want to explain!). Maybe we haven't looked hard enough, maybe we haven't look in the right place, or maybe dark matter is just wrong.
The CMB has been a huge issue for dark matter alternatives. Previously, only dark matter had a good explanation. If this result holds, it could be an amazing leap forward is outlining the alternative types of theories that could explain cosmology.
> While dark matter is currently our best explanation, it is deeply flawed
Calling it deeply flawed is focusing on just one aspect of it. The name just refers to the darkness in our knowledge about what it is. We don't know. It might be a form of matter, it might be a new factor in our equations or something completely different.
there's definitely some weird shit going on with "conventional dark matter theories". For example, aside from the fact that both are mysterious, there is no a priori reason for "the same phenomenon" to explain
- matter chunkiness at the universe-size scale
- rotational discrepancies at the galaxy-scale
yet it seems to be taken as gospel that lambda-CDM explains both. Please correct me if I'm wrong about this.
You're right that there could be multiple things which separately explain the things that dark matter explains (not just the two you listed, but the others as well: gravitational lensing, galaxy cluster motion, etc). But the strength of the dark matter model is that it can explain all of these phenomena; which is why most physicists prefer dark matter over other theories. It's very easy to come up with a theory which explains a single phenomena, but very hard to come up with one that simultaneously explains multiple phenomena.
To play devil's advocate, the strength of a model alone is not sufficient: I could say: Well, how can we be certain "gravitational waves" detected by LIGO aren't random dark matter density ripples and not GW from events we haven't correlated (n=1 on independent correlations). In other words, the dark matter model is too strong, because there is a arbitrarily parametrizable density field... Hell, there are people postulating Sagittarius A* is a very dense ball of DM and not a black hole. At that rate you can explain anything with dark matter. I have no logical or philosophical basis for this but in general when this sort of thing starts happening I start doubting the validity of a concept, not gaining confidence in it.
1. the 6th grade formula for total gravitational force and resulting orbital velocity for 2 spherical balls (one having mass of the galaxy, the other - our target star) at large distances accurately describes the gravitation and orbital velocity of a star inside the disk. Well, it is not. One has to integrate/sum over all the stars and matter in the galaxy (though each star's and remote gas region's contribution into the total force toward our target star can be calculated using that 6th grade formula, so no MOND or the likes is needed) to calculate the gravitational force of the whole galaxy acting upon our target star. The disk shape results in the significant "discrepancy" from the "2 spherical balls" model predictions. The thinner the disk the larger the "discrepancy" - more DM as its proponents claim.
2. the galaxies are fixed rotating bodies, and the stars orbit the Bulge on fixed orbits. They aren't. The galaxies evolve with the disk becoming wider and thinner with time (more and more DM/"discrepancy"). Just like a spiral wheel firework. That is exactly what happens when stars' velocity is higher than would be needed to maintain fixed orbit (i.e. what the 6th grade formula would suggest). Btw, that also means that 2 billion years ago when the life appeared on our planet the Solar system was much closer to the Bulge, not in the deserted suburbia that we're right now.
> If this result holds, it could be an amazing leap
I'm not sure if one can use the term result here. In the paper there is just a write-down of a theory that is deliberately designed to match an extra couple lines of astrophysical evidence that previous write-downs incorporating Milgrom's function (see https://arxiv.org/abs/1112.3960 for a partial catalogue of dozens of families of them) did not. Indeed, the paper's abstract says this clearly: "We discuss phenomenological requirements leading to [the theory's] construction and demonstrate its agreement with the observed [CMB & matter]".
The theory in the paper doesn't match all the troublesome-for-relativistic-MOND lines of evidence (choosing to focus on CMB polarization) and the paper's authors are uncertain about several. See e.g. the first paragraph (starting at its third sentence) in the Discussion section on p. 5 and the subsequent paragraph. Note (weak field) quasistatic approximation. They carry on to an admission that they struggle to suppress unlikely imprints on the CMB, and propose to introduce further dark fields to do so. These fields will have their own density distribution and dynamics. The only really nonstandard thing is that they have a strong preference for treating these as gravitational degrees of freedom (modified gravity) rather than generators of stress-energy (matter).
From a theorist's perspective it's neat that they were able to do this, because it's been known for a little more than fifteen years that it's hard to write down such a theory and have it be apparently self-consistent. It is not, however, apparently complete. Indeed, returning to your "there is something fundamental ... we don't understand", the paper says: "Absence of ghosts to quadratic order signifies a healthy theory that could arise as a limit of a more fundamental theory. We do not have such a theory at present".
The ghost condensate they go on to discuss is essentially a non-zero average correction to the values predicted by their theory in the low energy limit. Specifically they appear to be trying to control the non-Gaussianities in the CMB associated with their scalar's dynamics corresponding to an aether (yes, really) having a rest frame that is not the CMB rest frame. (Their unit-timelike vector field A^\mu also breaks invariance under Lorentz boosts, which probably impacts ultra-high-energy cosmic rays if extragalactic, leading to different ghosts.)
> predicts ... an entire class of matter that we've been unable to find any physical proof for other than cosmology (and cosmology is the thing we want to explain!)
This objection shows up often in online forums, but seems to ignore the pattern of discovery of particles that do not participate in electromagnetism.
Roll back to ~1930 where we want to explain the statistics of beta decay and have Pauli postulating a particle which wasn't previously observed in nuclear physics, and defied observation for forty-five years. Or to ~1910 when people were scratching their head over the atomic masses of heavy water and other chemical isotopes leading to the proposal of a proton-massed electromagnetically uncharged particle. Neutrinos (non-relic) are hot dark matter. If they were heavy enough not to zip away from galaxy clusters, they'd be cold WIMPs. If free neutrons didn't decay so quickly, with a suitable distribution (bb relic field?) they could also be candidates for WIMP cold dark matter, and also their discovery by 1932 (i.e. before Bevatron or at least the larger Berkeley deuteron cyclotrons) would seem optimistic.
There may be good reasons to doubt particle cold dark matter, but that it hasn't been detected in the 40 years since Peebles proposed it does not seem like one.
Additionally, particle physicists are looking for a variety of new particles to solve totally non-gravitational problems in the Standard Model. Several of these could be good candidates for particle cold dark matter. Indeed, cold dark matter could turn out to be a mix of several of these. Who knows? It'll be fun finding out.
> I hope there's lots of fundamental things we don't understand well yet.
I suppose there are many ways one could define "fundamental," but if you define "fundamental things" to be roughly "answers to questions of the form 'How does X work?' or 'Why are things this way instead of some other way?'" it seems clear that there can never be an end to fundamental things we don't understand yet.
What happened to the recent work showing that galactic rotation curves are consistent with ordinary GR? Last I read, cosmologists were choosing to ignore it. The article does not mention it, and treats galaxy rotation as if it were still considered anomalous.
It would be amusing if dark matter and MOND turned out to be both correct, and both needed. E.g., dark matter is diffuse enough not to affect galaxy rotation, but clumped enough to account for lensing and cluster adhesion.
Casting MOND as a matter of fields, which are also particles, seems to mean just a different sort of dark matter that interacts by some other means than gravitation, rather than our model of gravity itself being off. Some people who dislike dark matter would not like that much.
> What happened to the recent work showing that galactic rotation curves are consistent with ordinary GR? Last I read, cosmologists were choosing to ignore it.
Gravitomagnetism is a well-understood and experimentally measured effect. It is also a very small effect, of the order v^2 / c^2 where v is the speed of the sources. In the galaxy, stars move with v/c ~ 1/1000, which means the gravitomagnetic correction is one in a million. So while N-body simulations do sometimes account for general relativistic corrections like these, they're not nearly large enough to remove the requirement for dark matter.
That is the simple reason the paper has been ignored by everyone in the scientific community and rejected from decent journals. Of course, this hasn't stopped hundreds of fluffy pop articles being written on it, or it getting posted every week on HN. The blind leading the blind.
What I am hearing is that nobody has found an error in his derivation; instead, everybody has chosen to continue skating on the v^2/c^2 estimate arrived at without having done the detailed maths.
In general, anytime mathematical rigor is at issue, I will prefer to bet on the plasma fluid dynamicist over the cosmologist.
"please be MOND, please be MOND, please be MOND... " page loads "YES!"
I've always had a soft spot for MOND. A friend of mine (now tenured at STScI!), once pointed out to me that it was really fringe, and, for more than a decade hence, I've also thought of it as a wonderful and intentionally self-deprecating example of how otherwise seemingly "rational" people can believe in superstitions.
For those interested in an introduction to the world of cosmology, MOND vs Dark matter, etc, I highly recommend the book "Cosmic Revolutionary"[0].
The premise is "okay, you have a theory to explain everything better. Here's all the data we've collected that you need to match to make your theory be accepted".
It's very approachable and really taught me a lot. It gives you what you need to read stories like this better.
Why is Hacker News so fixated on MOND? I mean, I guess general relativity is hard for general public, but come on...
At this point MONDs look like really overfit models, failing to make any observable predictions, struggling to describe what we already observe (by overfitting)
the biggest point is: you are telling me there is something that makes up the majority of matter in the universe (27% dark matter vs 5% matter) and we still haven't observed a single iota of it, even after spending more than 3 decades and billions of dollars?
'well it fits all of our understanding of the universe and what we observe in a few things'
It comes on top of things that cosmologists have been wrong for very very very long times on. Look how long they thought it was silly to consider the big bang. maybe it would be easier to accept if they were like 'well the big bang is a very interesting idea but it just doesn't fit evidence' instead of 'that's a stupid idea, my idea (static universe) is simpler so its right'.
speaking of which, we really need to get off this 'simple idea is the right idea' dogma. The universe owes us no such obligation to be simple.
cosmology got so many assumptions baked in them its hard to figure out where they begin and end. for example, look how much relies off the idea that the universe is the same everywhere, which we now know as wrong, but cosmologists are only slightly admitting to that fact.
> you are telling me there is something that makes up the majority of matter in the universe (27% dark matter vs 5% matter) and we still haven't observed a single iota of it, even after spending more than 3 decades and billions of dollars?
Of course we observed it. In how galaxies spin. We did not observe dark matter directly. So far existence of dark matter is not questioned because it is backed by multiple predictions and observations. Question is about its composition.
> well it fits all of our understanding of the universe and what we observe in a few things
Not sure what it means.
> It comes on top of things that cosmologists have been wrong for very very very long times on. Look how long they thought it was silly to consider the big bang. maybe it would be easier to accept if they were like 'well the big bang is a very interesting idea but it just doesn't fit evidence' instead of 'that's a stupid idea, my idea (static universe) is simpler so its right'.
This is gross oversimplification to the point where it loses all meaning. I can't even begin to answer because it.
> speaking of which, we really need to get off this 'simple idea is the right idea' dogma. The universe owes us no such obligation to be simple.
I guess General Relativity is complex enough that most still try to drag what they learned in high school to fit reality
> look how much relies off the idea that the universe is the same everywhere, which we now know as wrong, but cosmologists are only slightly admitting to that fact.
Did I missed a Nobel Prize for proving cosmological principle wrong? Because so far all I seen was an overwhelming evidence for its correctness.
>'simple idea is the right idea' dogma. The universe owes us no such obligation to be simple.
You aren't wrong, but the simple answer is a really good heuristic. Its just, when you're wrong, you're gonna be really wrong and it'll be almost definitionally interesting and noteworthy.
I thought it was the strong equivalence principle in general relatively, or the (nameless?) assumption that the same laws of physics hold true everywhere.
Regardless, my question was about the part of the quote which said: "which we now know as wrong."
What aspect of the cosmological principle, strong equivalence principle, or the universal application of physical law do we now know to be be wrong?
Its the idea if you take one slice of the universe, it should be the same as any other slice. in this case, not talking about different physics but different makeups.
then they noticed that the spin of galaxies is correlated. like one pie in the sky of galaxies tend to spin left, and the next one tends to spin right, and the next one after that left again. as far as I know, its unsolved as to why. some think it might be that the observed galaxies are spinning around something much bigger that we have yet observed, others think its an influence by the cosmic web.
the idea that the universe is the same as everywhere (although an assumption) is very much baked in lots of theories, including the arguments that support dark matter.
This is not my subfield so I may be talking out of my depth, but it feels like you are conflating two different concepts. There is a physics assumption that laws are universal, then there is a cosmological assumption that energy distribution after the Big Bang was (near-)uniform. Dark energy and dark matter follows mostly from the physics assumption not the cosmological one.
perhaps the topology of spacetime and usual assumptions of some kind of constant (or no) curvature everywhere as apposed to something with more complex curvature?
wait, what? Are you seriously saying MOND is an overfit and LCDM isn't? MOND is gravity + 1 free parameter, and this theory adds one more free parameter. Conventional dark matter generates a "distribution of dark matter" that is set on a per-galaxy basis, so each galaxy gets its own parameter space. The classic rebuttal against the MOND is that LCDM has the freedom to explain galaxies with "too much" and "too little" dark matter, which gets to exactly that point.
Whatever you think of MOND, dismissing it as an overfit model, given how LCDM works, is really strange.
Why don't you peeps check out some of the explanations coming from plasma physicists and electric engineers that have oberserved similarities between their fields of expertise and things going on on earth, it's atmosphere and space (sun, planets, stars)?
There is actually a model, that doesn't need dark matter and such things, which is called plasma cosmology or electric universe.
The rotational aspect of galaxies is pretty easily explained with knowledge about plasma, loaded particle clouds and an understanding of electricity.
The best thing is, they can actually predict stuff.
Contrast that with dark matter theories and gravitational models.
Check out the SAFIRE Project https://safireproject.com/ for an interesting experimental take on the sun.
Electric Universe is crankery: they cherry pick their examples, there is no unifying theory, they reject making mathematical predictions, and they ignore substantial evidence which contradicts them. What's more, astrophysicists are not unaware of electric and magnetic fields (as is often claimed by EU theorists), and model them frequently when they are relevant.
Please lead me to some examples for your claims, if you have them, so I can make up my mind and re-evaluate my stance, if you're correct.
I'd appreciate it.
I'll start with some comments for non-experts, and then escalate about ten paragraphs further down.
tl;dr: there are lots of things that hang on General Relativity being correct practically everywhere in our universe, the only "hiding places" that don't break astrophysical objects (or even laboratory experiments, including in robotic laboratories we have sent to other places in our solar system) is very close to the big bang, deep inside black holes, and in large masses brought into a quantum superposition of space.
The core of General Relativity is a mathematically-complete relationship between matter in a spacetime, and spacetime curvature. The key point is that the exact relationship can be described correctly at every point in the spacetime.
The relationship takes on a particular form: the Einstein Field Equations (EFE), which can be written (omitting prefactors, the cosmological constant, and indices) as G = T, where "G" is the Einstein curvature tensor and T is the stress-energy tensor. G and T are really tensor fields, which take on a value at every point in a spacetime. T encodes the matter content at a given point, and can represent incredibly complex "piles" of interacting particles or matter field values.
The slogan form of this is, "moving matter generates curvature, curvature moves matter". The result is that setting out distribution of matter that obeys some dynamical laws generates spacetime curvature. But there can additionally be "vacuum-generated" curvature around which one might sprinkle some matter, which would then be entrained into orbits or other trajectories by that curvature. The latter is the approach used in the study of theoretical black holes, for example. But also it's a good way to understand the expansion of space: there is a "vacuum-generated" expanding spacetime curvature, with galaxy clusters distributed through it, and entrained into trajectories principally by that curvature.
We can also look at trajectories, and with the assumption that all matter falls the same way ("the universality of free-fall"), recover the curvature, the distribution and dynamics of the stress-energy, or both. This is quite common in astrophysical settings, where one is trying to determine an equation of state for a body like a white dwarf or a neutron star.
One of the problems that particle Dark Matter seeks to solve is that gas and stars far from the centres of galaxies of do not fall in faster than they do. Something holds them up, keeping them on unexpected (non-Newtonian) trajectories. We can model this by introducing extra complexity into the stress-energy tensor, starting with something simple and abstract and drilling down where evidence allows us to do so. One might write this as G = f(T), some function on the dark-matter-free matter content matches the curvature exactly. We can improve upon an initial simple f() over time. But alternatively we can explore f(G) = T.
It's been known since the 1920s that the relationship at the core is pretty flexible: we can choose a background curvature (flat spacetime, a black hole) and add matter and see what happens, or we can start with a distribution of matter (and dynamics) and see what it does to the Einstein curvature tensor. We can (a) encode more and more complicated representations of matter into the stress-energy tensor, and keep curvature simple. Or instead, (b) we can adapt the curvature making the "background" more and more complicated, and then sprinkle a relatively simple distribution of matter on top.
(Particle) Dark Matter is mainly the (a) approach. We assume that a galaxy's curvature is fairly simple in the bulk, lay out a reasonable model of the bulk visible matter of a galaxy (and electromagnetic radiation, and neutrinos), and then ask, "What must we do to the stress-energy tensor so that we still generate the observed trajectories of outermost matter (gas, dust, stars)?".
MOND is mainly the (b) approach. There is an extremely simple empirical law (from Mordehai Milgrom in 1981) that adapts Newtonian gravitation to generate the non-Newtonian orbits of outermost stars observed in most spiral galaxies. This may translate into a function on the Einstein curvature tensor that produces a "background" in which a realistic description of a galaxy's visible matter (and electromagnetic radiation and neutrinos) is kept from being flung out into intergalactic space. The problem is that it turns out one cannot do this while keeping General Relativity's exact relationship between matter and curvature, because keeping Milgrom's constant means matter at the outsides of galaxies feels gravitation (and other interactions) differently from matter in for example the solar circle (the part of the Milky Way where we find our sun's orbit, about 8.5 kiloparsecs from the core), or in the central parsec.
I'll expand on this by quoting [1] (Stacey McGaugh, second author, is a MOND proponent quoted in the aps.org article), "The heart of GR is the equivalence principle(s), in its weak (WEP), Einstein (EEP) and strong (SEP) form. The WEP states the universality of free fall, while the EEP states that one recovers special relativity in the freely falling frame of the WEP. These equivalence principles are obtained by assuming that all known matter fields are universally and minimally coupled to one single metric tensor, the physical metric. It is perfectly fine to keep these principles in MOND, although certain versions can involve another type of (dark) matter not following the same geodesics as the known matter, and thus effectively violating the WEP. Additionally, note that the local Lorentz invariance of special relativity could be spontaneously violated in MOND theories. The SEP, on the other hand, states that all laws of physics, including gravitation itself, are fully independent of velocity and location in spacetime [...] This principle has to be broken in MOND."
SEP also means WEP holds, and WEP requires that gravitational mass and inertial mass are identical for all bodies including self-gravitating ones like planets, stars, neutron stars, and so on.
A few pages along [2], Famaey & McGaugh write, "It is perhaps more important that, if MOND is correct in the sense of the acceleration a_0 [Milgrom's law's constant] being a truly fundamental quantity, the strong equivalence principle cannot hold anymore, and local Lorentz invariance could perhaps be spontaneously violated too."
That is, relativistic MOND generally means you lose the guarantee of Special Relativity holding in a small neighbourhood around every point in spacetime, which is liable to affect tests of the Standard Model of Particle Physics (which has that guarantee fundamentally baked in). Worse than that, with SEP violation, in general laws of physics must vary depending on a probe's proximity to mass, particularly probed bodies' response to acceleration. This is awkward given recent astrophysical evidence supporting the SEP (e.g. [3]).
In order to accord with evidence in favour of the SEP, one has to do some handstands, adding complexity to the function on curvature.
Of note to experts is Skordis & Zlosnik p. 5: "The vector in (5) does not seem to obey gauge invariance but in the quadratic action (13) it does so through mixing with diffeomorphisms of h_munu" and "The resulting action is that of the gauged ghost condensate (GGC) [122] or bumblebee field [123, 124] which has been proposed as a healthy gauge-invariant theory of spontaneous Lorentz violation."
from which one can jump into https://en.wikipedia.org/wiki/Bumblebee_models#Nambu%E2%80%9... (which is decently encyclopedic) and relate that to the quote at the top's argument that in a relativistic MOND, either Special Relativity isn't a guarantee in the small neighbourhood around every point (it is guaranteed by General Relativity, and is highly tested) or we recover it by adding more fields to the replacement of the \Lambda-equipped Einstein-Hilbert action.
I gather the idea is to suppress significant violations of the Strong Equivalence Principle, and to do so by adding yet more degrees of freedom.
From Famaey & McGaugh again [at [2]], "it is true that it would be more elegant to avoid too many additional degrees of freedom", which we can relate to K Freese's quote in the aps.org article.
Finally, quoting Skordis & Zlosnik again, "Studies of MOND with galaxy clusters [...] report that either a_0 is larger in clusters and/or an additional dark component is necessary even when the MOND prescription is used [...] the theory presented here has additional features warranting its separate testing with clusters." [Emphasis mine]
Thank you. This is the first explanation of gravity I've read that isn't overly simplistic (e.g. analogies about cats) yet it's technical enough to help my understanding without going deep into mathematical notation that is beyond me.
Good question! It's the stress-energy that generates curvature, and matter is just short hand for stress-energy or energy-momentum. Matter remaining at e.g. the origin of spatial coordinates (x=0, y=0, z=0, t=var) is still moving through spacetime [1]. T^{tt} encodes the flux of energy-momentum through the point along the time direction, and identifies as energy-density. Also, you get to think about if and how "remaining [at fixed] spatial coordinates" is actually meaningful in relativity.
"Don't rely on slogans" is a good General Relativity slogan.
is it not the case that we can't be sure if lorentz invariance holds? IIRC there are completely consistent solutions to GR where the speed of light is anisotropic, which breaks lorentz invariance.
Thank you for putting this as a question. I'll try to answer.
GR is not restricted to describing our universe. It deals in general curved spacetimes, an infinite number of which are manifestly unphysical, a classic example being the Gödel solution of 1949. Physical applications of General Relativity require one to impose a number of constraints, most of which are motivated by evidence. I will restrict myself here to the constraint you asked about.
Our universe is up to measurability and for all practical purposes Lorentzian (3 spacelike and one timelike dimension), giving us local time-orientability. Our universe cannot be non-orientable for a variety of reasons, including the highly investigated parity symmetry breaking in the neutrino sector. The gaps in which one tries to hide from this are small and shrinking. This is a strong constraint, and it was felt when investigating SUGRA (especially the 11-dimensional maximal SUperGRAvity) as a physical theory.
The unit-timelike vector in the paper discussed in The Fine Article can, without constraints, break local time-orientability. One could grind out consequences of this, but it's not easy to do (and the authors do not do it in this paper). One might, for example, need a mechanism to suppress the popping-up of light right-handed neutrinos [1], or at least their impact on astronomical spectra and terrestrial studies of isotopes. I'd think one would want to do that in the matter side of the EFEs rather than the curvature side, but partly it's a matter of aesthetics and ease of use, and partly it's "you introduced curvature which has the effect of changing the observables predicted by the Standard Model, including regularly confirmed observables; you should repair the damage with curvature (and the obvious thing is to just hit 'undo')".
There are many other natural phenomena that serve as probes of local Lorentz invariance violation ("LIV"), which I am sure you can find if you are interested. https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_vi... is a decent jumping off point. One might note that there is a lot about neutrinos there.
GR can certainly completely consistently describe spacetimes of different dimension, different (or non-)orientability locally and globally, and so forth. There are good reasons to study 2-dimensional and 3-dimensional spacetimes instead of the 4-dimensional one we inhabit. There are fun reasons to study timeless, many-timed, and/or many-spaced spacetimes[1b]. There have been reasonably well-motivated-by-physics reasons to study extra spacelike dimensions.
I'm not sure what your threshold of "be[ing] sure" is, but mine is certainly met. It would be a tremendous (and cool) surprise if LIV were to be shown experimentally or implied in extreme astrophysical observations, and even more so within our (less extreme) solar system.
Finally, I turn to your IIRC, which is not correct. General Relativity has a single metric to which everything couples. This is the root of the universality of free fall part of the Strong Equivalence Principle. In General Relativity we can only vary the (vacuum) speed of light by giving light a rest mass. Most Variable Speed of Light (VSL) approaches introduce new objects into the field equations, making a theoretical alternative to General Relativity. Examples include bimetric theories, which add a metric of constant curvature and typically other scalar and/or vector fields; different massless species can couple to the different metrics, and if the constant curvature is Minkowski (flat), then Special Relativity is preserved on a per-sector basis, with complicated intersectoral interactions. There are a variety of other approaches, Magueijo 2003 https://arxiv.org/abs/astro-ph/0305457 is an overview that springs to mind.
[1b] ibid., §2.2 (pdf page 18) is the start of an extended discussion of how one might couple realistic matter (in this section a toy non-interacting (except gravitationally) field, but heading towards the full Standard Model in later sections) into non-Lorentzian universes.
Hm. I was mostly thinking about Tangherlini relativity. I know him personally and he once talked to me about it, I only got the very basics and then lost him when the math got complicated. It doesn't seem to be in the review.
Given that space is expanding in all directions, isn't it almost guaranteed that the Higgs field has a vector component, like particles in a rising loaf of bread do?
> Consider requirement (iii), that is, successful cosmology. In (2) we have a new d.o.f. φ [...] What should the expectation for a cosmological evolution of ϕ be? The MOND law for galaxies is silent regarding this matter. There is, however, another empirical law which concerns cosmology: the existence of sizable amounts of energy density scaling precisely as a^(−3).
In other words, they are saying that to get the cosmology right, they need to add stuff that behaves exactly like dark matter -- that is what they are alluding to with the "sizable amounts of energy". They make their φ field play this role. It's just like TeVeS, the other major relativistic MOND theory, where the scalar "S" field does the same thing.
The popular press likes to frame the debate as "dark matter vs. modified gravity", but it's really "dark matter vs. dark matter plus modified gravity", which is much less dramatic.