[He, Jian-Hua; Wang, Bin] Shanghai Jiao Tong Univ, INPAC, Shanghai 200240, Peoples R China; [He, Jian-Hua; Wang, Bin] Shanghai Jiao Tong Univ, Dept Phys, Shanghai 200240, Peoples R China; [Wang, Bin] Chinese Acad Sci, Kavli Inst Theoret Phys China, Beijing 10080, Peoples R China; [Abdalla, Elcio] Univ Sao Paulo, Inst Fis, BR-05315970 Sao Paulo, Brazil
We examine the conformal equivalence between the f(R) gravity and the interacting dark sector model. We review the well-known result that the conformal transformation physically corresponds to the mass dilation that marks the strength of interaction between dark sectors. Instead of modeling f(R) gravity in the Jordan frame, we construct the f(R) gravity in terms of mass dilation function in the Einstein frame. We find that the condition to keep f(R) gravity consistent with CMB observations ensures the energy flow from dark energy to dark matter in the corresponding interacting model, which meets the requirement to alleviate the coincidence problem in the Einstein framework.