Focusing on the local type primordial non-Gaussianities, we study the bispectrum and trispectrum during a non-minimal slow-roll inflation. We use the so-called δNformalism to investigate the super-horizon evolution of the primordial perturbations in this setup. Firstly we obtain the main equations of the model and introduce the framework of the δNformalism for this case. Then we give analytical expressions for the nonlinear parameters describing the non-Gaussianity in the slow-roll approximation. We analyze the bispectrum by its non-linear parameter, fNL. Furthermore, we calculate τNLand gNLwhich are non-linear parameters characterizing the amplitude of trispectrum. Finally, by adopting a quadratic form for both the potential and non-minimal coupling (NMC) function, we test our setup in the light of Planck2015 data and constrain the model parameters space. The non-Gaussianity parameters obtained in our setup are so small, consistent with recent observation. We extend our analysis to see the situation in the Einstein frame and compare the results in these two frames.
