Non-trivial extension of Starobinsky inflation

We consider a non-canonic field in the context of Starobinsky inflation. We work in Einstein-frame. In this frame, the gravitational part of the action is equivalent to the Hilbert-Einstein action, plus a scalar field called scalaron. We investigate a model with a heavy scalaron trapped at the effective potential minimum, where its fluctuations are negligible. To be more explicit, we consider a Dirac-Born-Infeld (DBI) field, which is usually considered within the brane inflation context, as the non-canonic field. Although, the DBI field governs inflation through implicit dependence on Scalaron the boost factor, and other quantities are different from the standard DBI model. For appropriate parameters, this model is consistent with the Planck results.