Is it certain that dark matter consists of particles? (And not just curved space) 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?
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 &amp; Duda (2011).