The $R+R^2$ model of gravity with the corresponding shallow potential in the
Einstein frame is consistent with the observations. Recently, many effort have
been made to generalize the $R+R^2$ (Starobinsky) model of inflation or use
other shallow potentials to construct a model for the early Universe. We revise
the question about the shallow potential. We propose a model in which the
Starobinsky model can emerge through a dynamical mechanism. We show that the
absence of ghost modes results to constraints on the parameters of the
Starobinsky model. We obtain the scalar spectral index and the tensor-to-scalar
ratio of the extended model and study the three-point correlation function of
the curvature perturbation to estimate the primordial non-Gaussianities of the
proposed model.
