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Following Edwin Hubble, it is widely believed that the universe is expanding, which is based on the red-shift of light from distant objects. Can dark matter cause light to be red-shifted and make it look like the universe is expanding while in fact it is not?

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Short-short version: No. Dark matter is "dark" because it does not interact electromagnetically.

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As @Kyle says below, this is not true. Dark Matter does gravitationally influence light, though the effect is very weak. But as he also says in the answer below, this is very unlikely to be the explanation behind the cosmological redshift, as the effect is simply much, much too weak. Writing this here instead of a downvote; this answer is misleading. –  Thriveth Jun 5 '13 at 15:28
    
@Thriveth The small red-shift that occurs while climbing out of galactic gravity well certainly exists, but it is the same for all galaxies of a given mass and geometry. That is it doesn't vary by distances except to the degree to which the distribution of galaxies is affected by distance. But that goes the wrong way as the early universe had more small, light galaxies than the present epoch. More-over there is a corresponding blue shift as the light comes down into the gravity well of the Milky Way (which being a big, heavy galaxy may outweigh the shift at the origin). –  dmckee Jun 5 '13 at 15:34
    
I am not going to disagree with you on any of that, but I didn't write it out because it was already very well explained in the other answers. I see now that I was quite unclear, though. The only thing that I didn't like about the answer was that it says a categorical 'no', which could lead the reader to believe that DM doesn't affect light at all. It was really just a matter of nuances, though I see now that I formulated myself a bit too sharply.. –  Thriveth Jun 5 '13 at 15:41
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Dark matter does cause light to be red-shifted via gravitational redshift. The best example of this that relates to dark matter is light emitted from other galaxies (or clusters of galaxies, or any structure that is expected to he hosted in a dark matter "halo"). A photon emitted near the center of a deep gravitational potential well needs energy to "climb out" of the well; the required energy is released by a redshift of the photon. There is of course a corresponding blue-shift for a photon falling into a potential well.

A slightly more complicated example is for a photon passing through a galaxy cluster. As the photon falls into the cluster, it experiences a blueshift. Clusters are large, so it takes quite a long time (a few to tens of Myrs) for the photon to get across. During this time the cluster will typically accrete some mass, deepening its potential, so on the way out the photon will experience a redshift of a magnitude greater than the blueshift it experienced on the way in. A photon passing through a galaxy cluster therefore experiences a net redshift.

I gave these two examples because they are relevant to the second part of the question - could dark matter make the Universe appear to expand while in fact being static? The idea of an expanding Universe is indeed motivated by the observation that more distant galaxies have higher redshifts. The first example I gave doesn't scale the right way - it actually scales the other way since more massive structures form at later times, so we observe more massive structures nearby and these are the ones giving the strongest redshifts.

The second example actually does scale the right way because clusters accreted mass faster at earlier times than they do today, so the strongest redshifts from this effect will be from structures observed as they were a long time ago - those furthest away.

The reason we can't explain away cosmic expansion with all this is that the magnitude of gravitational redshift that we predict and observe in these scenarios is very small - much smaller than the redshift we attribute to cosmic expansion. Either the Universe is expanding, or something very fundamental about our understanding of gravity is flawed (my opinion is that the former is true, but people do research alternate theories of gravity; so far no breakthroughs, though).

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BTW, this " Clusters are large, so [...] the cluster will typically accrete some mass, deepening its potential, so on the way out the photon will experience a redshift of a magnitude greater than the blueshift it experienced on the way in." doesn't work. At least in the weak field approximation the asymptotic shift is zero whatever the configuration of the mass was because you can model it as a interaction which each bit separately. Things don't get added to a cluster ab inito, their gravitational effects were present as they approached. –  dmckee Jun 5 '13 at 15:41
    
Hm had to think about that a bit, but you're right. The obvious exception is if you stick a black hole in the middle of the cluster so that the photon never gets out the other side, but that's stepping well outside the weak field approximation. Anyway I'll leave the answer as-is with your comment as an (important!) caveat, thanks. –  Kyle Jun 5 '13 at 17:53
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Let us assume momentarily that your hypothesis is true. One consequence is that dark matter in different galaxies would redshift light by different amounts, in high correlation with the second distance measure given by luminosity of the baryonic matter in the galaxy. So you are back to correlating dark matter to distance, anyway. Unlikely.

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