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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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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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    $\begingroup$ 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. $\endgroup$
    – Rody Oldenhuis
    Commented Aug 27, 2012 at 7:23
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    $\begingroup$ Occam says its matter. Granted, we don't know the details. $\endgroup$
    – kleingordon
    Commented Aug 27, 2012 at 20:59
  • $\begingroup$ @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. $\endgroup$
    – kleingordon
    Commented Aug 27, 2012 at 21:28
  • $\begingroup$ 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. $\endgroup$
    – Rody Oldenhuis
    Commented Aug 28, 2012 at 3:55
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    $\begingroup$ But the dark matter hypothesis buys you more than just a wave of the hands. It allows us to understand the dynamics of the unknown stuff in to a framework with which we can make theoretical predictions, and does quite well in that regard (see also adsabs.harvard.edu/abs/2012Natur.487..202D). It allows us to consider different equations of state for the matter, and allows us to conclude based on observations and simulations that the dark matter is non-relativistic. This explanation tis more compelling than a statement that space-time just curves on its own. $\endgroup$
    – kleingordon
    Commented Oct 2, 2012 at 5:34

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