Which hypothesis?
Sorry, this one:
That number is just directly calculated from the already measured dark matter density, assuming particle-based dark matter and the mass assumption stated.
For directly detecting the particles passing through in an individual way, there is a very active and diverse field of experimental research trying to do just that. We don’t know how massive individual dark matter particles may be nor how strongly they may interact with normal stuff (although there is some guidance based on the astrophysical and cosmological requirements), so it’s a matter of continually improving detection techniques to increase the range of masses and interaction strengths that would be detectable. These experiments generally involve very controlled environments and bleeding-edge particle detector technologies.
So the answer would be “Hard enough that we are still refining the bleeding edge tech that’s required”
In my more cynically despairing moods I wonder if the anomalous movement of galaxies will remain forever unexplained. No candidate for dark matter particles will ever turn up, and no theoretical dark matter extensions to the Standard Model will ever be testable. “Dark Matter” will simply be a hole in science, forever. A wizard did it.
More or less, yes.
Some techniques would benefit directly from simple up-scaling of their size (which is a money question rather than a tech question), but some techniques are exactly like you say: they are very much pushing the technical frontier.
The universe is a simulation and the programmers just added a fudge factor to make it work without thinking too much about it.
I encourage you to look at the “evidence for dark matter” link I posted above. “Anomalous movement of galaxies” was the first twinkle of a problem. Today, dark matter’s influence is seen in a wide array of observational channels to form a fantastically consistent picture of the evolution of the universe and the structures within it.
(It’s the difference between, “Hmm, I hear some scratching in the attic. Rats?” to where we are today, which is, “I hear scratching at regular times of the night, and there is a chew-hole in the attic vent screen, and there are these ripped up pieces of insulation all over, and there are squeaking sounds that stop when I open the attic hatch, and there are bits of scat around. Rats?” We maybe haven’t seen the rat directly, but there is definitely a rat.)
Except we will never, ever actually see a rat. We will have to postulate rats who not only are invisible but never do anything while there are witnesses around. And postulate a theory of invisible ghost rats that is otherwise 100% ad hoc, untestable, and at odds with the rest of our understanding of how reality works. Dark Matter is almost that bad.
But… it isn’t. The astrophysical and cosmological evidence (the latter of which is harder to appreciate, to be sure) is absolutely overwhelming, much more so than some other facts in science where you wouldn’t be skeptical in the slightest. The so-far non-detection in terrestrial detectors is 100% consistent with the other incontrovertible evidence of the rat, er.., dark matter. If we stick to the half-baked rat metaphor, it’s as if we only have ladder technology at the “step stool” level, so we can only peek into the attic from a very poor vantage point. We know we may not see the rat directly yet. That’s fine. That’s no reason to claim all the piles and piles of rat data we do have is somehow invalid.
ETA: And this is why people are actively building better “ladders”. It’s not because we aren’t sure if dark matter is there; it’s in fact because we are sure. It would be very cool to directly see the rat, so that we can understand more of its detailed properties. But that task is on top of the fact that we already know the rat is there.
EDIT: Eureka! So that’s what dark matter is!
Neutrinos also interact via the weak force. Those interactions, though rare and weak, are how we know they are there. They also have a very small mass. So small that despite their huge numbers, there aren’t enough of them to account for dark matter.
Short answer: the GR equation Einstein used to describe the orbit of Mercury has the precession just fall out plop.
I saw a video a while back that is perfect for the layman in explaining how the GR field equations lead to this outcome (maybe Veritassium?). If I find it, I’ll post it. I think it is exactly what you’re looking for.
What if…
…we assume gravity radiates in four dimensions…not just from mass from back in the past and forwards in the future, but also sideways from alternate realities (Many Worlds Theorem).
Spacetime distorted by mass other than the three-dimensional matter we can directly “see”.
Back in the 1980s, I took a minicourse that took us through the calculation - it was cool.
I’ve seen that idea used in science fiction - but it was hand-wavy (John Cramer’s “Twistor”)
Then gravity would decay with distance according to the square-cube law, it would decay according to the square-quart(?is that right? To the 4th power instead of the 3rd, I think that’s “quarted” rather than “cubed”) law.
Likewise, in a 2d universe, gravity would decay more slowly with distance (I want to say linearly but I’m not sure that’s right).
I may be mistaken but I think the definition of a parallel universe is that it doesn’t interact with ours in any way, if it does is not really another universe.
I share your incredulity. Having read further in the thread that the deviation that needed to be explained is only one hundredth of a degree per century I am amazed that this would be noticed even today.
Brian Greene says the reason gravity is so weak is that all the other forces are confined to 4-dimensions but gravity extends into multiple dimensions. 10 or 11 depending on who you ask.