You have probably heard of dark matter. It is the stuff that is supposed to be the predominant matter of the Universe, but nobody has ever managed to find any, which is a little embarrassing when there is supposed to be something like about 6 times more dark matter in the Universe than ordinary matter. Even more embarrassing is the fact that nobody has any real idea what it could be. Every time someone postulates what it is, and work out a way to detect it, they find absolutely nothing. On the other hand there may be a simpler reason for this. Just maybe they postulated what they thought they could find, as opposed to what it is, in other words it was a proposal to get more funds with the uncovering the nature of the Universe as a hoped-for by-product.
The first reason why there might be dark matter came from the rotation of galaxies. Newtonian mechanics makes some specific predictions. Very specifically, the periodic time for an object orbiting the centre of mass at a distance r varies as r^1.5. That means that say there are two orbiting objects, say Earth and Mars, where Mars is about 1.52 times more distant, the Martian year is about 1.88 Earth years. The relationship works very well in our solar system, and it was from the unexpected effects on Uranus that Neptune was predicted, and found to be in the expected place. However, when we take this up to galactic level, things come unstuck. As we move out from the centre, stars move faster than predicted from the speed of those in the centre. This is quite unambiguous, and has been found in many galaxies. The conventional explanation is that enormous quantities of cold dark matter provide the additional gravitational binding.
However, that explanation also has problems. A study of 175 galaxies showed that the radial acceleration at different distances correlated with the amount of visible matter attracting it, but the relationship does not match Newtonian dynamics. If the discrepancies are due to dark matter, one might expect the dark matter to be present in different amounts in different galaxies, and different parts of the same galaxy. Any such relationship should have a lot of scatter, but it hasn’t. Of course, that might be a result of dark matter being attracted to ordinary matter.
There is an alternative explanation called MOND, which stands for modified Newtonian gravity, which proposes that at large distances and small accelerations, gravity decays more slowly than the inverse square law. The correlation of the radial acceleration with the amount of visible matter would be required by something like MOND, so that is a big plus for it, although the only reason it was postulated in this form was to account for what we see. However, a further study has shown there is no simple scale factor. What this means is that if MOBD is correct the effects on different galaxies should be essentially dependent on the mass of visible matter but it isn’t. MOND can explain any galaxy, but the results don’t translate to other galaxies in any simple way. This should rule out MOND without amending the underlying dynamics, in other words, altering Newtonian laws of motion as well as gravity. This may be no problem for dark matter, as different distributions would give different effects. But wait: in the previous paragraph it was claimed there was no scatter.
The net result: there are two sides to this: one says MOND is ruled out and the other says no it isn’t, and the problem is that it is observational uncertainties that suggest it might be. The two sides of the argument seem to be either using different data or are interpreting the same data differently. I am no wiser.
Astronomers have also observed one of the most distant galaxies ever, MACS1149-JD1, which is over ten billion light years away, and it too is rotating, although the rotational velocity is much slower than galaxies that we see that are much closer and nowhere near as old. So why is it slower? Possible reasons include it has much less mass, hence the gravity is weaker.
However, this galaxy is of significant interest because its age makes it one of the earliest galaxies to form. It also has stars in it estimated to be 300 million years old, which puts the star formation at just 270 million years after the Big Bang. The problem with that is it is in the dark period, when matter as we know it had presumably not formed, so how did a collection of stars start? For gravity to cause a star to accrete, it has to give off radiation but supposedly no radiation was given off then. Again, something seems to be wrong. That most of the stars are just this age makes it appear that the galaxy formed about the same time as the stars, or put it another way, something made a whole lot of stars form at the same time in places where the net result was a galaxy. How did that happen? And where did the angular momentum come from? Then again, did it happen? This is at the limit of observational techniques, so have we drawn a non-valid conclusion from difficult to interpret data. Again, I have no idea, but I mention this to show there is a still a lot to learn about how things started.