[part 2/2]

The result discussed at the link above comes from study of a the X-ray luminous and large MACS J1149.5+2223 from the MAssive Cluster Survey (MACS, <https://iopscience.iop.org/article/10.1086/320958>), redshift ~ 0.544 (around 5 billion light-years distance). As with most massive clusters, platforms like Hubble have observed multiple images of background (even more distant) bright objects near the centre of the galaxy cluster. The centre is found by looking at the proper motions and other features of its constituent galaxies, and the centre is relatively transparent. These features aren't surprising in a dark matter paradigm (some DM settles to the centre of the cluster and tends to draw gas and dust into large black holes; more generally, transparent lines of sight through the cluster between its galaxies aren't vacuum: they have some density of dark matter like all shiny or background-obscuring parts of the cluster). Relativistic MOND theories struggle with this in different ways, with different possible repairs to the relativistic theory (one can also add some dark matter to most of these theories; some of these theories may allow there to be less dark matter than visible matter).

Determining the mass of this particular MACS cluster is hard in any theory, and multiple images of background objects with predictable features (e.g. the "Refsdal" supernova, with a predictable light-curve, in the link at the top) help. The mass (and its distribution) and other features of the cluster can pin down the distance of multiply-lensed background objects. Theories which imply different cluster masses (e.g. no DM at all == much much less mass) should have different image multiplicities and the images appearing at different locations; this also varies the distance to the background objects.

> cmb estimate

Well, we can fix the evolution of the expansion of the universe to some value and compare observations to predictions of various theories of cosmology. There are parameters in \Lambda-CDM (the "concordance" model, which deliberately tracks new discoveries) that are not known to great precision; altering these constants, converting everywhere-everywhen constant parameters to scale-factor-dependent parameters, and so forth, all result in a cosmos with different features. As we discover features of our own cosmos, we'll adapt the standard/concordance model of cosmology.

Not only can one depart from \Lambda-CDM without departing from General Relativity, one can also replace General Relativity in an effort to eliminate the \Lambda parameter, or Cold Dark Matter, or both. One can then see if observed features are allowed in the non-concordance theory, or whether straightforward attempts to extract such features concord with astrophysical evidence. Also, one can see if the non-concordance theory predicts features that there is no evidence for (and which the concordance model does not predict).

> is this a result in favor of dark matter over mond

The paper is mostly about the Hubble tension. Newtonian-limit + dark matter vs modified Newtonian dynamics + no dark matter isn't a great comparison here because the multiply-lensed-by-massive-cluster supernova simply is not a system in the Newtonian limit (and in several ways).

Instead one might ask if this is something in favour of \Lambda-CDM vs a no-dark-matter (and maybe no dark energy) alternative relativistic theory of gravitation. The answer: maybe. It's easy to understand in \Lambda-CDM (see above), but perhaps that's because experience with that theory has developed intuitions (and comparable intuitions might arise if using a different set of theories). But the question of how a non-General Relativity theory of gravitation work far from the (modified) Newtonian weak-field/low-velocity limit bites in several places; there are lots of moving parts at different distances and scales (at the very largest scales visible matter looks smooth, but it gets lumpy when one zooms in and sees voids, filaments, galaxy clusters, and so forth) and getting it right at all scales is more useful than getting it "more right at least for now" at just a couple of scales but not getting it "at least as right" at others. Making concordance cosmologies based on various alternatives to General Relativity is at best a set of works-in-progress. But the general-relativistic standard cosmology is also a work-in-progress, so perhaps comparisons are more practical (what's easier to work with?) or maybe metaphysical.

From a practical perspective, relativists are very used to throwing up their hands and resorting to a more complicated model of stress-energy ("matter") than they really want to calculate with. In some relativistic systems in (~stellar) astrophysics it really does matter how Yukawa coupling works, and you can't just say "oh, stiff liquid here". There are lots and lots of mechanisms which generate stress-energy, many of which were unknown even sixty years ago. Stress-energy sources the gravitational field, which is relatively simple in GR compared to alternatives like scalar-tensor/vector-tensor/scalar-vector-tensor/scalar-tensor-vector/tensor-vector-scalar (yes, these are all real theories and they're all different!), bi- and multimetric theories, non-metric theories and so on. How does moving matter vary the mathematical objects? Sometimes that's a hard question, especially if the matter is very dense, very energetic, or moving at large fractions of the speed of light. But it's the central question.

Finally, if you're keen on Hubble tension, this is an excellent 2021 review: <https://iopscience.iop.org/article/10.1088/1361-6382/ac086d>

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[1] Hodson, Zhao (2017), Generalizing MOND to explain the missing mass in galaxy clusters, <https://arxiv.org/abs/1701.03369> §1, para 4,5- is a good recent overview.

[2] Negrelli et al. 2020, Testing Modified Gravity theory (MOG) with Type Ia Supernovae, Cosmic Chronometers and Baryon Acoustic Oscillations <https://arxiv.org/abs/2004.13648>.