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Could someone please explain briefly or refer me to an article or manuscript that shows how $f(R)$ modified gravity theories can be used to explain the problem of dark matter, particularly the galaxy rotation problem?

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I already checked that out, could you suggest more. – MrDi May 12 '14 at 18:48
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The Wikipedia article lists thirty references. Have you looked at any of them? – rob May 12 '14 at 18:52
    
Have you tried ADS? Or Google Scholar? Or any search engine? – Kyle Kanos May 12 '14 at 19:24

I quite enjoyed this article that contrasts the standard $\Lambda{\rm CDM}$ cosmology and $\rm MOND$ (for other flavours of modified gravity, you'd have to look elsewhere). The author does a pretty good job of stating the cases for and against both theories. Figure 4 may be of particular interest. It's not very technical, so if you want a derivation of the predictions of $\rm MOND$ you won't find it here, but it is well referenced, so it might point you somewhere interesting.

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