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I always very much enjoy these posts with many upvotes and few comments.
I upvoted here 50% because I found it interesting, 50% because I wanted to hear criticism from people knowledgable on the matter and 50% because I'm actually too stupid to fully comprehend it and hope for an ELI5 (as you may tell, I'm not hot on math).
WRT ELI5 (and bear in mind I'm a layman who's only briefly skimmed the article, but this may do till an expert chips in, corrections welcome):

There are a couple of main ways of calculating the speed of the expansion of the universe; they are very different and act at different scales, but should obviously tally. They don't, and the mismatch is often referred to as a crisis in cosmology in popular articles on the subject. It's a serious issue because each of the two different methods is foundational in our understanding of the structure of the universe in their domain; we can't just prefer one over the other.

Our standard way of modelling the universe relies on Einstein's general relativity in a larger framework that caters for dark matter; a (controversial) "Newtonian" alternative is called MOND and this article proposes ways that elements of the two (but favouring the latter) might be combined to counter the discrepancies in the measurements, taking into account other difficulties in the process like the void in the title.

Further reading;

Crisis: https://www.quantamagazine.org/cosmologists-debate-how-fast-...

MOND https://www.wikipedia.org/wiki/Modified_Newtonian_dynamics

Standard Cosmological Model https://www.wikipedia.org/wiki/Lambda-CDM_model

Another ELI5 by someone not at all qualified to understand this stuff (I.E. a layman).

We know from measurements of the leftover energy (CMB) approximately how long ago the big bang happened, and how fast it appears to be expanding. Our most favored model of the universes physics, General Relativity makes certain predictions that mostly match up with reality up until you get to galaxy scales at which point they start to diverge. In order for our measurements to work under General Relativity our galaxies need to be more massive than they appear to be based on all the stuff we can actually see in them. This needed excess mass is called dark matter, but even with dark matter the universe appears to be expanding faster than it should. The theory proposed in the paper is that the universe as whole isn't actually expanding faster, but due to a quirk of where we are in the universe it only looks like it is when we look at nearby galaxies. Unfortunately for that to be true we would need to be in a void in the structure of the universe which General Relativity predicts shouldn't be possible.

An alternative theory of universal physics exists called MOND. MOND is similar to General Relativity, but rather than solving the problem at the galaxy scale through theoretical dark matter, it instead just assumes that gravity works differently once you reach a certain cutoff point. This aligns with observations of actual galaxies (not entirely unsurprisingly because the cutoff point was chosen in order to align with those observations) without needing dark matter to exist. From the perspective of the paper there's another nice property of MOND which is that simulations based on it allow for the kind of void to form that the paper predicts would be necessary to explain the locally observed expansion.

Basically, General Relativity can't explain how fast galaxies spin without Dark Matter, nor how fast the universe appears to be expanding. MOND combined with our galaxy being in the middle of a big void can explain both. Both theories, General Relativity and MOND require a certain amount of hand waving in order to align with reality. MOND requires a bit less but is highly suspect because it's solution is basically "gravity just acts different sometimes" which is suspiciously close to "it's that way because it is".

As for the actual math involved in all of this, beats me, we'll need to wait for someone who's actually in this field to look it over and explain what if anything is wrong with it all.

Isn't there also observational data that disfavors MOND?

I remember it had something to do with galaxies colliding and the dark matter staying behind or something along those lines.

The bullet cluster is an n of one and the dark matter estimates come from redshifting/lensing, which could have come from other sources in such an unusual scenario.

Some of the other crazy observations like ultradiffuse galaxies are, on recalculation, not as extreme as initially guessed, and predicated on an indirect empirical estimate of mass (number of globular clusters) with no mechanistic confirmation.

Not sure honestly. That might have something to do with the vHDM theory mentioned in the paper. I didn't really follow a lot of it, but I think (major grain of salt here) it's saying that that theory predicts some very light neutrinos exist and tend to collect inside of galactic clusters, but not galaxies themselves and that it's those neutrinos that make up the missing mass at universal scales that general relativity explains using dark matter.

Either case seems pretty hand wavy honestly. When it comes to galaxy and universe level physics it all seems pretty weak compared to the sort of particle physics and classical physics that we can actually measure and test on Earth. It's all just a bunch of theoretical math with relatively few actual measurements to pin it all down. I don't think we're anywhere near having a solid theory of the universe so it's mostly an exercise in trying to prove which theory is the least wrong at this point, rather than which one is correct.

So General Relativity is a theoretical framework that has been proven to match observation[0], while MOND's details have been chosen to match observation, without any theoretical basis? Is that right? Or is there some mechanism proposed as to why gravity's cutoff point is where it is?

[0]up to a certain point, and if you include Dark Matter, which we still don't understand (the original assumption was that it was WIMPs, but as we still haven't found a WIMP that would do this, then we don't know what it is).

So, first thing, I'm not a astrophysicist nor even a physicist of any type, so I might be misunderstanding things here, but this is how I interpret all this. Hopefully if I've gotten something significantly wrong someone will correct it.

General Relativity matches observations to a point. The issue is that it stops matching observations once you reach galactic scales. In order to explain why that doesn't work you need to start hand waving, and the start of that is dark matter. MOND was thought up not so much as an alternative to General Relativity but as an alternative to dark matter. It tweaks some of the math used in General Relativity to assume that gravity behaves differently at different levels. Basically once you have a strong enough gravitational field it behaves like the gravity we know, but until you hit that point its effects diminish at a different rate. Doing that explains why galaxies behave like they do. For the bulk of the galaxy gravity is strong enough that it behaves exactly like General Relativity says it should, but out near the edges of the galaxy gravity has grown weak enough that it behaves differently. It's sort of hand wavy and leaves a bit of a bad taste in the mouth since there's no real explanation of why gravity should behave that way. On the other hand it doesn't require some phantom matter that we have no observational data to back up.

Either theory falls far short, and both of them require a lot of fudging around the edges to align with galactic scale observations, although MOND once you get past the arbitrary change to gravity seems to require less hand waving. Importantly for the linked paper it also seems to line up with the proposed theory and predict the kind of void the paper is predicated on which would be a strong point in favor of MOND.

Of key point to the proposed theory, General Relativity predicts that in the first moments after the big bang that the universe was essentially uniform, that everything spread out more or less evenly, and it wasn't until much later when things started to form the likes of planets and stars that we started seeing significant variation in matter distribution of the universe. MOND on the other hand allows for variation in that initial expansion. That's important for the paper because there simply isn't enough time in the General Relativity model to explain a void the size that their theory predicts would be necessary to form. MOND allowing for more variability early on on the other hand does allow enough time that a void of the necessary size could exist.

Basically General Relativity on its own doesn't work for things galaxy size and bigger. MOND on its own doesn't work at galactic cluster levels and above. The theory proposed in the paper could explain the discrepancy we see in the rate of expansion of the universe, but doesn't seem to be possible under General Relativity, but is possible under MOND. Both General Relativity and MOND rely on the presence of things not observed yet in order to match with our observations once you scale things back far enough, and neither on its own can explain why the universe seems to be expanding faster than they predict it should. The paper proposes one theory for that, but it's only possible with MOND.

As far as I understand the problem with dark matter is also that there isn't a single dark matter theory, but lots of different ones with a lot of very variable tunables. So the problem is that dark matter by itself isn't that predictive.
The term dark matter itself is kind of misleading in the first place. The math in general relativity just doesn't add up when applied to certain observations. They've essentially gotten 2 + 2 = 5. In order to fix that they just assume that one of those 2's was actually a 3 somehow, and the extra 1 it picked up got labelled as dark matter. In other words, dark matter is just a term for some missing numbers somewhere in the calculation. Based on the different places where the extra numbers might be included they think it's something with mass, but really that's just a guess based on the existing formula and the changes that would be necessary to make it match the observation.
Our very own Milky way is inside the KBC void [0] discussed in the article. It never ceases to amaze me that our local group [1], part of the local Laniakea supercluster [2], despite the hundred of thousand of galaxies it contains is almost empty space and part of the void!

[0] https://en.wikipedia.org/wiki/KBC_Void [1] https://en.wikipedia.org/wiki/Local_Group [2] https://en.wikipedia.org/wiki/Laniakea_Supercluster

Could this be why we exist? Aliens don't like to travel across space desert, it isn't worth their time and risk, so we are in an island of safety.
Grimdark fiction[0] aside, I doubt anything is traveling across intergalactic voids of any size.

[0]: https://warhammer40k.fandom.com/wiki/Tyranids

I saw an MIT PhD thesis defense video of a paper that described the calculations of how far/fast probes could spread between galaxies.

I really wish I could find it again... but my searches have failed.

The conclusion was that self-replicating probes could indeed populate (I forget how many - on the order of hundreds of thousands/millions) nearby galaxies within the last couple billion years.

It was pretty compelling. The discussion at the end did see some debate of "well then where are they?". A valid question. Why haven't self-replicating probes infected the entire visible universe by now?

wouldn't it be like we did with plastic bottles to the oceans? only imagine if the bottles could self-replicate. Pollution at intergalactic scale. Probably getting to specific levels of technology requires specific level of consciousness - a corresponding level of awareness about actions and consequences. A technological level increase without corresponding consciousness level increase is probably one of the great filters. Like for example human civilization failure to recognize the human civilization induced global warming.

wrt. original post :

>For ΛCDM to fit the pattern of fluctuations observed in the CMB by the Planck satellite and other experiments, the Hubble constant must have a particular value of 67.4 ± 0.5 km/s/Mpc. Local measurements are nearly all above this ‘Planck value’, but are consistent with each other. In our paper, we use a local value of 73.8 ± 1.1 km/s/Mpc using a combination of supernovae and gravitationally lensed quasars, two particularly precise yet independent techniques.

I think it is not an accident that c divided by the age of the universe (meaning that those stars have been flying away from us with constant speed c) produces 71km/s/Mpc. That also means that there is no acceleration nor deceleration - stars fly away from us with constant speed [Hubble constant x distance] with the distance growing and the Hubble constant decreasing resulting in the same speed for any given star.

Sounds pretty close to http://www.fhi.ox.ac.uk/wp-content/uploads/intergalactic-spr...

Who is to say there isn't such a probe in the solar system currently? Said probe could be watching earth for promising or dangerous signs and deciding what to do.

Considering the hundred billion stars in our galaxy, it’s hard to imagine if there were threatening alien life anywhere in the universe that it wouldn’t be in our own galaxy.
Nice one!!! Never thought of it that way. On the other hand I now feel more isolated, knowing our civilization is just a flower in the desert that most probably no one is going to notice.
At this scale this seems an unlikely explanation, given that we are in an oasis of the 'desert' containing hundreds of thousands of galaxies.
Is there a galactic equivalent of a solar system's heliosphere?
Yep, but we cannot send probe to measure it boundaries yet.
As much as I am fond of MOND (hu hu), is this going to get any traction? It seems like the MOND and lCDM worlds have stopped trying to interact with each other, covering their ears and going "bla bla bla" while building parallel and non-interacting lines of research.
I feel like (as someone not too well versed in cosmology) that bigger and better telescopes and interferometry can help to validate stuff like MOND. in particular as it relates to better measurements of galactic structures.