How is it that a wormhole thread comes around to dark matter so much? Anyway, Morrus and Umbran have already made nice posts, but this will be my take.
I'll admit I don't have a complete idea of everything done in the field - that would take more time than I have available - but I'm not exactly a layman either. I have been a professional researcher in the past and I'm pretty familiar with how things go, at least in my domains of knowledge (control theory, inertial navigation, optics, acoustics). After chatting with a mathematician friend last year about dark matter, I was interested enough to spend an afternoon reading up on what's been done. What I read reminded me of personal experiences where social dynamics among the people involved drove the direction of research as much as the data does. As you said, it makes sense to look into every possibility, but in the stuff I read, at least, it looked like the possibility that the gravity model needed to be modified had almost been ignored, with 99%+ of research effort looking into dark matter rather than other possibilities. Even now the alternatives to dark matter are considered very much fringe science. Whatever the truth turns out to be, I don't think that giving almost all research effort to looking for something that had never in any way been observed rather than giving some effort to investigating the possibility that the theories were incorrect was a good idea.
With all due respect, I don't think you can get a fair picture of what's been done in an afternoon even with the research background you have. And I don't think your mathematician friend has one either, unless he/she is actually an astrophysicist or particle physicist of the right type. Here is my disclaimer: I am a university professor of physics, and half of my research program is particle physics related to dark matter. I get research grants to carry out that work; those grants
do not pay my salary, but they do pay some of my students (on the grand scale of things, I am pretty small potatoes, but whatever). That said, dark matter was something I picked up after about a decade of work on other subjects, and it took me quite a while to become fully conversant with the details of the evidence and current work. There is a lot going on! My point is just that there is a lot of detailed analysis that people really do check over independently. This is science done the same way all good science is done.
But, anyway, here's the story:
Dark matter was first discovered in the 1930s. No one believed in it at the time. People were probably not convinced by the measurements (errors were large at the time, and in fact the numbers were off compared to current measurements).
It took 35 years for the idea to come up again due to (better) measurements in somewhat more controlled systems (orbits of stars in galaxies as opposed to more random motions of galaxies in clusters). At that point, it was fair to say that the measurements could be explained by a new particle that does not interact with light, dark matter, or a modified gravity theory, which I will call MOND after the most prominent.
Now we have other measurements besides stars in galaxies. We have:
1) Galaxies in clusters. Motion of galaxies is well explained by a similar amount of dark matter as in galaxies (in proportion to normal matter). MOND that explains galaxy rotations can explain clusters only if you also postulate some additional matter that does not interact with light --- dark matter again. Maybe there is an epicycle that fixes this problem; I see differing claims.
2) Gravitational lensing of light passing galaxies and clusters of galaxies. Again, this is well explained by the expected amount of dark matter and not by MOND. A famous example is the bullet cluster, which is really two clusters colliding. The prediction of dark matter theory matched the observations. MOND predicted something else, though I will say its adherents quickly came up with a tweak to match the observations pretty quickly after the fact.
3) The overall structure of the universe matches very well with simulations that include the expected amount of dark matter. There are multiple types of measurements to support this. Something related is the following.
4) The prediction of dark matter theory matches in extreme detail observations of the cosmic microwave background, which is relic light that gives us a good picture of the universe when it was very nearly uniform. Because of that uniformity, physics was in many ways simpler then than now, so its relatively easy to make predictions for the CMB given some theory. And those measurements just can't work without a different source of gravity than normal matter. Even some high profile proponents of MOND theories have admitted that modifying gravity without dark matter just can't explain these observations. I should note that CMB observations of sufficient detail were not done until 2000 and later, long after dark matter was first really accepted.
So, here we have quite a few observations made over decades of history. There are two sets of theories to explain them. One, dark matter, was calibrated by the first accurate measurement and subsequently did very well predicting the results of later observations. The other, MOND or modified gravity, was calibrated very well to the first measurement and didn't do very well at all with subsequent ones. Yet people still study it (I see papers on it reasonably often) because it does well on the galaxy level. But I hope you can see in a limited way why there is so much work done on dark matter. It is the Occam's razor theory.
Then there is the issue of whether it's crazy to invent a new type of particle and look for it. Here's my response. To have the chemistry we know, we only really need 4 types of particles: electrons, protons, neutrons, and photons. But instead protons and neutrons are made up of a couple of types of quarks held together by gluons. That's really all you need. But we have also discovered neutrinos, which are totally different and weird in their own way. And muons, which are just like electrons but about 200x heavier. And taus, which are still just like electrons but even heavier. And 4 more kinds of quarks. None of these really had to be there. The equations work better with two additional force carriers for some nuclear interactions, and we found them. Same thing for the Higgs boson. But 2/3 or more of the "matter" particles are just there, and we don't know what principle says they should be there. So is it that strange to say there might be one more type of particle? Especially since there are hints in the equations and experiments that physics might just work better with some more particles of specific types that include some that could reasonably be dark matter?
Well, I hope that's enough for you to read for one night.
