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Is there a model of modified gravity that either was close to or have succeeded in modelling the problem of dark energy, and suffers from no instabilities and explains the observational data. Also has the approach to use modified gravity to explain the problem of dark energy been abandoned?

Needed to write a review about the challenges facing modified gravity, Any insight would be great. Cheers

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AFAIK, modified gravity models were developed to eliminate the need of dark matter (very different from dark energy) by introducing either spatially-dependent gravitational accelerations or higher order terms in the Einstein-Hilbert action. –  Kyle Kanos Apr 25 at 1:36
    
@KyleKanos modified gravity also includes things like f(R) theories and quintessence, which are developed to explain dark energy –  Jim Apr 25 at 3:05
    
are there any successful models that tried to explain dark matter or dark energy? –  user28952 Apr 25 at 3:38
    
Define "successful." –  Kyle Kanos Apr 25 at 13:06
    
By successful I mean that It doesn't suffer from instabilities and other problems and explains the expanding universe. –  user28952 Apr 27 at 15:23
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I uploaded a paper titled "A cyclic cosmological model based on the f(ρ) modified theory of gravity" (arXiv:1106.0341) in 2011.

Please judge by yourself if it meets your criteria: (A) It close to or has succeeded in modelling the problem of dark energy (and dark matter), and (B) suffers from no instabilities (no singularity) and (C) explains the observational data (solar system), (D) explains observational data (early inflation and later accelerated expansion).

-mike

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