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Dark Matter appears to have more in common with phenomena related to spatial geometry then a particle. I thought in General Relativity, space can be curved without the presence of matter so gravitational lensing does not imply there is matter present but that the space in a region is curved. If Dark matter has more characteristics related to spatial geometry, why is it referred to as a kind of exotic particle (WIMP).

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possible duplicate: physics.stackexchange.com/questions/29459/… –  Michael Brown Mar 25 '13 at 3:26
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There are 2 popular approaches to this puzzle called the dark matter problem. First is through a modification to general theory of relativity as you had suggested. The second is through postulating presence of an unseen particle. I would suspect an unseen particle is the more likely reason for observed experimental discrepancies like galaxy rotation curves being flatter than expected. –  Prathyush Mar 25 '13 at 3:46
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You're right that gravitational lensing, and really any large-scale stuff involving gravity, tells us directly about spacetime rather than the stuff out there.

But spacetime, according to GR, is constrained by the mass, energy, momentum, pressure, and shear. The equation we write down is $$ G_{\mu\nu} = 8\pi T_{\mu\nu}, $$ which unfortunately means almost nothing if you don't already know GR, but it just feels so good to write down people like me can't help it sometimes. Basically, the left side encompasses curvature and all that, while the right deals with the "stuff." Inferences about curvature therefore tell us something about the "stuff" there.

Our observations tell us there is a lot of "stuff" that has mass, moves slowly, and does not interact with light. We call it dark matter. Once you believe there is something with mass out there, quantum mechanics tells us we can probably think of it as a particle (i.e. an excitation of a quantum field, to be pedantic) on some level.

Beyond this, our models of cosmology work incredibly well when we postulate that there are particles out there that have mass and only interact via the weak force. These models include everything from the details of the cosmic microwave background to the clumping of matter into galaxies on large scales. Could you come up with some other explanation? Perhaps. But there is a lot of evidence coming from different directions pointing toward WIMPs of some sort.

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Could you come up with some other explanation? Yes. Goto: Math Overflow: Is there a mathematical expression for orbital rotation between two concentric vortices? How do you vote in advance to close or remove the most important document of this century? –  user4884 Mar 25 '13 at 11:10
    
The observational evidence you are referring to has to be interpreted by mathematical models and simulations. WIMPs are based on the Standard Model's idea of Supersymmetry. The evidence coming out of the LHC does not support super symmetry. So goes Super Symmetry so goes WIMP's and String Theory as well. –  user4884 Mar 25 '13 at 14:50
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@user4884: WIMPs have little to do with supersymmetry. They are just hypothetical particles that do not feel the strong force or the electromagnetic voce, and are massive enough that they are moving much more slowly that light speed. While it is true that string theorists and supersymmetry proponents put forth a number of candidates for WIMPs, the evidence for WIMPs is independent of these theories. This is an excellent answer. –  Peter Shor Mar 25 '13 at 15:32
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