We thank Clifford Will for inviting us to write this article in Living Reviews in Relativity. We are grateful to Luca Amendola, Kazuharu Bamba, Bruce A. Bassett, Gianluca Calcagni, Salvatore Capozziello, Sean M. Carroll, Edmund J. Copleand, Beatriz de Carlos, Vikram Duvvuri, Damien A. Easson, Stephane Fay, Radouane Gannouji, Chao-Qiang Geng, Jean-Marc Gerard, Burin Gumjudpai, Zong-kuan Guo, Mark Hindmarsh, Maxim Libanov, Roy Maartens, Kei-ichi Maeda, Gianpiero Mangano, Shuntaro Mizuno, Bruno Moraes, David F. Mota, Pia Mukherjee, Nobuyoshi Ohta, Eleftherios Papantonopoulos, David Polarski, Christophe Ringeval, Valery Rubakov, M. Sami, Pasquale D. Serpico, Alexei Starobinsky, Teruaki Suyama, Takashi Tamaki, Takayuki Tatekawa, Reza Tavakol, Alexey Toporensky, Takashi Torii, Peter Tretjakov, Michael S. Turner, Mark Trodden, Kotub Uddin, David Wands, Yun Wang, and Jun’ichi Yokoyama for fruitful collaborations about f (R) theory and modified gravity. We also thank Eugeny Babichev, Nathalie Deruelle, Kazuya Koyama, David Langlois, and Shinji Mukohyama for useful discussions. The work of A.D. and S.T. was supported by the Grant-in-Aid for Scientific Research Fund of the JSPS Nos. 09314 and 30318802. S.T. also thanks financial support for the Grant-in-Aid for Scientific Research on Innovative Areas (No. 21111006).
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