Large Non-Gaussianity in Non-Minimally Coupled Derivative Inflation with Gauss-Bonnet Correction

We study a nonminimal derivative inflationary model in the presence of the Gauss-Bonnet term. To have a complete treatment of the model, we consider a general form of the nonminimal derivative function and also the Gauss-Bonnet coupling term. By following the ADM formalism, expanding the action up to the third order in the perturbations and using the correlation functions, we study the perturbation and its non-Gaussian feature in details. We also study the consistency relation that gets modified in the presence of the Gauss-Bonnet term in the action. We compare the results of our consideration in confrontation with Planck2015 observational data and find some constraints on the model's parameters. Our treatment shows that this model in some ranges of the parameters is consistent with the observational data. Also, in some ranges of model's parameters, the model predicts blue-tilted power spectrum. Finally, we show that nonminimal derivative model in the presence of the GB term has capability to have large non-Gaussianity.