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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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Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

I already checked that out, could you suggest more. – MrDi May 12 '14 at 18:48
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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