  Although $f(R)$ modification of late time cosmology is successful in
explaining present cosmic acceleration, it is difficult to satisfy the
fifth-force constraint simultaneously. Even when the fifth-force constraint is
satisfied, the effective scalar degree of freedom may move to a point (close to
its potential minima) in the field space where the Ricci scalar diverges. We
elucidate this point further with a specific example of $f(R)$ gravity that
incorporates several viable $f(R)$ gravity models in the literature. In
particular, we show that the nonlinear evolution of the scalar field in
pressureless contracting dust can easily lead to the curvature singularity,
making this theory unviable.
