Modified gravity would not cover the main case for dark matter, though, which is not galaxy formation or patterns of motion we observe. Rather the main case is

Modified gravity would not cover the main case for dark matter, though, which is not galaxy formation or patterns of motion we observe. Rather the main case is the ratio of protons and neutrons to photons produced during Big Bang nucleosythesis. We know the ratio of the number of protons to number of photons. We know the number of photons in the universe (most of them are in the CMB), and we therefore know the number of protons. That means we know the amount of "normal" matter in the universe, and it is far less than the total amount of matter in the universe (that survived from baryogenesis). This requires there to be "dark matter" in the universe. The other effects like galaxy formation and stellar motion in galaxies are just things that might be caused by dark matter (though that's come into doubt, as Sabine points out). The real reason to believe in dark matter is Big Bang nucleosynthesis. Sean Carroll discusses it here: https://youtu.be/tZQadPmTd84?t=4642 https://youtu.be/tZQadPmTd84?t=4642