Is there a problem with interpreting dark matter as hidden dimensions?
Is there any solid, scientific counterargument against the hypothetical explanation that attributes dark matter as matter in hidden planes of existence?
I am trying to construct a world in which there are creatures and objects similar to ordinary objects (physically, if not biologically), and they are normally hidden in different spatial planes where only gravity can pass through, thus appearing like dark matter.
The kind of "matter" in the hidden dimension would resemble monsters and spacecrafts of a fashion not too deviant from human imagination, they also supposedly inhabit planet-like bodies, although that would not be required.
I wonder if there is any counterarguments in physics that will undermine this construction, for example, could one refute this claim by pointing out the fact that an amount of matter packed as densely as dark matter appear to be packed would surely form black-holes or other intelligible structures like stars and planet which should cause gravitational lensing effect that is different from what is observed.
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This has been proposed, believe it or not. Gravity is the weakest of the four fundamental forces, a mystery which has been dubbed the hierarchy problem. Several solutions have been floating around; one is that there are large extra dimensions through which gravity propagates. Gravity behaves according to the inverse square law in three dimensions (in the Newtonian approximation from a point source), and as $$F\propto\frac{1}{r^{n-1}}$$ in $n$ dimensions, so as $n$ grows, the force should get weaker. If gravity is the only force that can travel between dimensions, this solves the hierarchy problem. This is a case of brane cosmology, where the universe is represented as a surface embedded in higher-dimensional space, possible adjacent to other universes.
It can also be taken a step further to imply that matter from these other dimensions should interact with matter in "our" dimensions through gravity, mimicking dark matter. This fits in well with non-baryonic dark matter theories, as dark matter doesn't interact with normal matter through the electromagnetic force. Brane cosmology implies that the other three fundamental forces are "confined" to the surface of the branes. This solves the hierarchy problem by assuming that gravity "leaks", for lack of a better word, through these extra dimensions.
Fun anecdote: Models of astronomical observations over a decade ago by Qin et al. (2005) were interpreted by the authors as being evidence of three extra dimensions. Dark matter particles wouldn't directly travel through them, but would interact through the extra dimensions. The scientific community is very much not convinced. The observations still require dark matter to exist, but simply to be something that can self-interact in these extra pathways, so not quite what you're looking for, but similar.
This should not be confused with the idea of compactified extra dimensions (think tiny, rolled-up dimensions), which have also been proposed to explain dark matter. This would lead to these strange things called Kaluza-Klein states, which could be dark matter particles (see e.g. Cornell et al. (2014), although I haven't read the paper - it's largely beyond me!).
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