That’s the argument I think. Per that Wikipedia link:
> Randall hypothesizes a plane of dark matter exists roughly on the plane of the Milky Way galaxy. As the Sun oscillates in its orbit around the center of the galaxy, it passes through the dark matter.
If you're not smack bang in the middle of the galactic plane, you're going to be accelerated towards it by gravity, so you'll tend to bob up and down, like a pendulum.
The oscillations are not "around" the plane, they are through the plane.
That is; the plane itself has a local gravitational attraction
which is orthogonal to the galaxy core gravitational attraction.
If a mass is above or below the plane, the "local" gravity will
pull towards the plane.
since nothing stops it at the mid line of the plane it passes through
to the opposite side; rinse and repeat.
This bouncing above and below center line of the disk
is more or less independent of our solar system completing galactic orbits.
The up down oscillation is completely decoupled from the orbit itself, assuming the orbital potential is uniform. It's like the galaxy wasn't rotating at all. You put something above the disk, and it gets accelerated downwards, but doesn't stop at the disk, it keeps going, until it gets dragged back up. Think of it like a pendulum.
I haven't done the math but I would think it's possible due to interactions from other solar systems. Similar to how satellites oscillate around Lagrange points
I don't think that's really an accurate description. There's a discrepancy between observations relating to gravitation and general relativity's predictions. The discrepancy could be accounted for by significant extra mass, but no non-gravitational observations seem to confirm the presence of that extra mass. So "dark matter" is the supposition that there's a significant amount of extra mass that interacts only with gravity but not, for example, light, making it categorically different from ordinary matter. And I don't think there's any evidence that this dark matter follows the same gravitational constant as ordinary matter.
It does not matter whether it "follows the same gravitational constant as ordinary matter" or not.
For any kind of matter, normal or "dark", which is observed only through gravitational effects, you cannot determine separately its mass and the gravitational constant that applies to it. You can determine only the product between mass and gravitational constant (which is the cause of measurable forces).
Therefore for many astronomical objects the product between their mass and the gravitational constant is known with a much greater precision than their mass (because the gravitational constant is known with very poor precision even for ordinary matter).
The same applies for "dark matter". You cannot compute the distribution in space of the mass of the dark matter, but only the distribution in space of the product between its mass and whatever gravitational constant is applicable to it.
So even if a different gravitational constant were applicable to "dark matter" that fact would be irrelevant for any mathematical model that is fitted to the observations.
Not quite. Dark matter is the hypothesis that the discrepancy between theory and observation is due to a form of matter that interacts gravitationally but not electromagnetically. So we can't see it, and thus "dark".
There are other competing ideas including a family of modified Newtonian dynamics models, but nothing comes as close as explaining the observations as dark matter does.
There was a paper recently that showed that the discrepancy may be the higher order terms from general relativity that is often neglected because they are believed to be small - but that idea still needs to be proven to work for a large variety of cases.
The observations in question for this Dark matter hypothesis include the rotation velocity of stars in galaxies and a few other things like gravitational lensing.
Dark energy is a different discrepancy with theory. It's a term that we have to add to Einstein's field equations to account for the observation that the universal expansion is accelerating instead of slowing down. Again there are competing hypotheses, like non uniform density on the largest scales, but nothing quite explains everything as dark energy.