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.

• Received 3 April 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.131302