Singularity problem with f(R) models for dark energy

In this Letter, I point out that there is a curvature singularity problem appearing on the nonlinear 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 a linearized analysis, except for the telltale growing oscillatory modes it causes. In view of this, the viability of many f(R) models in the current literature will have to be reevaluated.