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The main idea about dark matter today seems to be supersymmetry. That there exists a set of yet undiscovered fundamental particles which (in a mathematically most convenient way) mirror the particles already known.

But has it been established that dark matter consists of particles at all? Couldn't it for example be a continuous property of space itself in some regions? That some parts of space are curved without the influence of any particles or waves. Is anything but particles ruled out?

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Also asked at https://physics.stackexchange.com/questions/174080/how-do-we-know-dark-matter-isnt-curved-spacetime

Basically no. Or at least you can't have this idea and General Relativity. GR demands that you have something (matter/energy density) to cause the curvature. Curvature without cause is not part of the model. That's not to say that what you propose couldn't be true, but one would then have to ditch GR, which is a reasonably successful model (though some would argue that the dark matter problem is one of its biggest failures!).

I think a lot of parameter space has been ruled out for dark matter. We know it can't be baryonic from our understanding of primordial element abundances and also from the way it interacts (or doesn't interact) with normal matter in forming the basic structures in our universe on the right timescales. The microlensing surveys that have been conducted rule out large (planetary sized and above) dark matter bodies (and black holes, brown dwarfs, cold white dwarfs etc.), since to account for all the mass, these would produce lots of microlensing events that simply aren't observed.

An excellent primer on these topics has been produced by Garrett & Duda (2011).

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  • $\begingroup$ I don't think that's adequate. You can have nonvanishing Weyl curvature without matter/energy density anywhere in spacetime. The reasoning in this answer therefore must be supplemented with something else, e.g., an appeal to the Friedmann equations for the large-scale or perhaps Raychaudhuri equation for gravitational lensing. $\endgroup$ – Stan Liou Apr 7 '15 at 1:47
  • $\begingroup$ @StanLiou Thanks Stan. I've bitten off more than I can chew on this clearly. $\endgroup$ – Rob Jeffries Apr 7 '15 at 7:41
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In terms of dark matter, there are two notions which are incorrect. One is that dark matter is a clump of stuff traveling with the matter. The other is that dark matter does not interact with matter.

Dark matter fills 'empty' space. Dark matter is displaced by matter.

The Milky Way moves through and displaces the dark matter.

The Milky Way's halo is the state of displacement of the dark matter.

The state of displacement of the dark matter is also known as the deformation of spacetime.

The Milky Way's halo is the deformation of spacetime.

Dark matter is the physical manifestation of spacetime.

'Ether and the Theory of Relativity by Albert Einstein' http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html

"Think of waves on the surface of water. Here we can describe two entirely different things. Either we may observe how the undulatory surface forming the boundary between water and air alters in the course of time; or else-with the help of small floats, for instance - we can observe how the position of the separate particles of water alters in the course of time. If the existence of such floats for tracking the motion of the particles of a fluid were a fundamental impossibility in physics - if, in fact nothing else whatever were observable than the shape of the space occupied by the water as it varies in time, we should have no ground for the assumption that water consists of movable particles. But all the same we could characterise it as a medium."

if, in fact nothing else whatever were observable than the shape of the space occupied by the dark matter as it varies in time, we should have no ground for the assumption that dark matter consists of movable particles. But all the same we could characterise it as a medium having mass which is displaced by the particles of matter which exist in it and move through it.

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