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Conformal gravity is an "alternative" theory of gravity, where instead of using the Einstein-Hilbert action composed of the Ricci scalar, the square of the conformal Weyl tensor is used. It was originally designed to arrive at the inflationary cosmological models without the use of dark energy.

However, it was later noticed that the galactic rotation curves of a certain matter distribution commonly seen in galaxies can also be accurately predicted using the conformal gravity and without the use of dark matter, but where in addition to total luminosity of the galaxy and its mass used in the matter distribution, two new constants appear. However, both of the constants turn out to be universal and are found to be equal for all galaxies (within the errors permitted by the deviation from the assumed baryonic matter distribution).

A while ago it was widely reported that the Bullet Cluster lensing effects rule out the alternative theories of gravity and provide evidence for dark matter. Does conformal gravity sufficiently explain the lensing effects observed in Bullet Cluster or is it similarly ruled out?

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according to arXiv:1208.4972 published 2012-08-23, no one has done the calculations yet –  Christoph Jan 9 '13 at 15:07
    
@Christoph, where exactly? i search for 'Bullet cluster' on the pdf and could find only a link in the reference –  lurscher Jan 11 '13 at 18:31
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@lurscher: see section VII: The implications for galactic clusters have not been explored; I already sent you that quote two weeks ago, btw ;) –  Christoph Jan 11 '13 at 19:07
    
ah true, sorry about that :-) –  lurscher Jan 12 '13 at 2:58

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Based on what I've heard during a few talks, and from skimming what I can from papers like this, I think the answer is probably not. In essence, my understanding is that conformal gravity leads to a different form of gravitational potential from mass distributions---but it can't create potential gradients where there isn't mass.

If you look at a picture of the bullet cluster (e.g., from here), you can clearly see that the primary source of field is in an entirely different place than the baryonic matter distribution.

Bullet Cluster

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So does that mean it is ruled out? From what I have heard, one of the reasons why conformal gravity seems to reproduce the dark matter rotation curve profiles is that the iron sphere theorem does not apply and that matter outside can contribute to the potential. Given that, is it obvious how this misalignment means conformal gravity is ruled out? –  SMeznaric Jan 11 '13 at 18:02
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@SMeznaric I would say the Bullet Cluster is very damaging to all theories that claim there is no dark matter, precisely for the reason zhermes stated: you can change how potentials drop off with distance, but you can't create massive regions of attraction in the middle of empty space. Of course, you can always come up with some scenario, however implausible, to say the Bullet Cluster data is being misinterpreted. –  Chris White Jan 11 '13 at 18:10
    
@ChrisWhite That is true. I can see how this can rule out MOND theories, where you change the potential in a classical (Newtonian) way. I think conformal gravity is a bit different in this regard, as here you modify action to be the square of the conformal tensor from the Ricci scalar, which changes space-time around a matter distribution in a way potentially dependent on matter outside the distribution of interest. It's not obvious to me that this could not effectively change the lensing effects to reproduce the apparent shift in the Newtonian potential. Can you explain more on this? –  SMeznaric Jan 11 '13 at 19:06
    
@SMeznaric, you need a way to establish the two centers of mass in the bullet cluster as preferred locations -- separate from that of the normal matter. That would seem to require a conspiracy of extended matter to form these highly symmetric, spheriodal mass distributions in just the right place -- which is quite improbable. –  zhermes Jan 11 '13 at 21:54
    
@SMeznaric, It also seems to be the case that if potentials depended on distant objects in such a convoluted way, it would make the normal dynamics of galaxies and galaxy clusters very different. –  zhermes Jan 11 '13 at 21:56

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