  The $f(R)$ gravity models proposed by Hu-Sawicki and Starobinsky are generic
for local gravity constraints to be evaded. The large deviations from these
models either result into violation of local gravity constraints or the
modifications are not distinguishable from cosmological constant. The curvature
singularity in these models is generic but can be avoided provided that proper
fine tuning is imposed on the evolution of scalaron in the high curvature
regime. In principle, the problem can be circumvented by incorporating
quadratic curvature correction in the Lagrangian though it might be quite
challenging to probe the relevant region numerically.
