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Are \(f(R)\) dark energy models cosmologically viable? (English) Zbl 1228.83115

Summary: All \(f(R)\) modified gravity theories are conformally identical to models of quintessence in which matter is coupled to dark energy with a strong coupling. This coupling induces a cosmological evolution radically different from standard cosmology. We find that, in all \(f(R)\) theories where a power of \(R\) is dominant at large or small \(R\) (which include most of those proposed so far in the literature), the scale factor during the matter phase grows as \(t^{1/2}\) instead of the standard law \(t^{2/3}\). This behavior is grossly inconsistent with cosmological observations (e.g., Wilkinson Microwave Anisotropy Probe), thereby ruling out these models even if they pass the supernovae test and can escape the local gravity constraints.

MSC:

83F05 Relativistic cosmology
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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