  In this paper, I point out that there is a curvature singularity problem
appearing on non-linear level that generally plagues f(R) models that modify
Einstein gravity in the infrared. It is caused by the fact that for the
effective scalar degree of freedom, the curvature singularity is at a finite
field value and energy level, and can be easily accessed by the field dynamics
in the presence of matter. This problem is invisible in linearized analysis,
except for the tell-tale growing oscillatory modes it causes. In view of this,
viability of many f(R) models in current literature will have to be
re-evaluated.
