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There is a very similar question to this one: Is dark matter really matter?. But the particular aspect I'm asking about seems not to be mentioned there. So, here we go:

Does dark matter have to exist as matter? Or, is it possible that space-time is just naturally not flat, but slightly crinkled? Obviously heavy objects can bend space-time, and if, as a layman, I understand it correctly, this is what we perceive as gravity. What now, if space-time is naturally not quite flat, and we perceive this non-flatness as dark matter?

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Dark matter is only a temporary name to something weird outhere. – Mario Enrique Aug 27 '12 at 11:48
and dark energy for something really weird – Henry Aug 27 '12 at 11:51
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Related: physics.stackexchange.com/q/29459/2451 – Qmechanic♦ Aug 27 '12 at 12:00

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Everything we do understand about space-time, under the framework of General Relativity, suggests that it only bends in response to matter, radiation, and some sort of dark energy. In this understanding, space will "crinkle" if and only if one or more of these components is present. With that in mind, there are myriad observations of space-time bending due to the influence of an unidentified type of matter concentrated in clusters of galaxies. The answer to your question is "yes."

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Purely being the Devil's advocate here: we haven't observed the matter, we've just seen spacetime being affected in ways similar to how it would when matter would be there. It is likely that it actually is some form of matter, but until we have actual observations and a solid theoretical basis for it, it could be anything. – Rody Oldenhuis Aug 27 '12 at 7:23
Occam says its matter. Granted, we don't know the details. – kleingordon Aug 27 '12 at 20:59
@RodyOldenhuis If you want to simultaneously explain gravitational lensing observations, the bullet cluster, and CMB anisotropy measurements, you have to go through epic contortions of reasoning to arrive at any other conclusion than the presence of matter. – kleingordon Aug 27 '12 at 21:28
Yes, you don't have to convince me :) I'm just pointing out that you should keep in mind that dark matter and dark energy remain to this point somewhat "magical" explanations to our observations -- matter is only a model that fits the data really well. – Rody Oldenhuis Aug 28 '12 at 3:55
@kleingordon Wouldn't Occam rather say that it's not matter? It's not as mathematically or aesthetically pleasing, nor is it as interesting from a physics point of view, but from my understanding "That's just the shape that space-time came out of the big bang" (paraphrased) seems to be simpler than saying "There must be some invisible stuff that bends it into the shape we observe". No? – user1264 Sep 24 '12 at 5:59
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