[prerok]

Thank you for the explanation.

What I don't like about this, is that we take the observations, apply some custom guesses as to why the spacetime is folded differently and... there you go, your formulas now match. It smells too much like the explanation of geocentric system, where they invented that planets also circle around a perceived dot on their trajectory path and that happily coincides with the Earth's rotation.

I think what we are missing is that these behaviors need to be predictable. We don't know where these anomalies in spacetime curvature will be and why they are there. And as I stated in another comment here, I think dark matter is a bad name for the unexplained spacetime curvatures (warpings?, wrinkles?).

[jjk166]

Again, you're focusing on one small sliver of what dark matter is observed to do, and coming up with alternative explanations for that particular observation. There are a whole host of different observations of dark matter, and any reasonable competing theory needs to explain all of them. Modified gravity is the inelegant epicycle explanation, while dark matter is the simple alternative explanation in your analogy.

> I think what we are missing is that these behaviors need to be predictable. We don't know where these anomalies in spacetime curvature will be and why they are there.

But we do! We can see galaxies that have been stripped of their dark matter and we can find nearby the dark matter that was stripped. We can predict, based on our theory of dark matter where these gravitational anomalies will be, then we look there and lo and behold we see them. We aren't applying custom guesses to match our observation, the universe just happens to match exactly what we'd expect it to look like if it contained a bunch of matter that didn't interact with the electromagnetic force.

> I think dark matter is a bad name for the unexplained spacetime curvatures (warpings?, wrinkles?).

Dark matter isn't the space time curves, which aren't particularly special. All massive particles produce such warping, and we just call it gravity. Dark matter is matter (stuff that interacts with gravity) which is dark (does not interact with light). We would expect it, assuming it exists, to produce such warping of spacetime, which again is exactly what we see.