directly use what he gets in Einstein frame as his final result. However, for the models we are going to discuss about, as has been addressed in [@Gong:2011qe], the curvature perturbations in two frames are no longer the same. As will be seen below, the difference is mainly due to the generation of isocurvature perturbations. Therefore, when the Einstein frame analysis is done, it is necessary to pull everything back to its Jordan frame to get the right results. In like manner, we also have to perform the constraint on observable in its Jordan frame with observational data.

Although some basic inflationary models has been checked against the observational data by the newest PLANCK Collaboration [@Ade:2013lta; @Planck:2015xua], many other models, including the ones we’re talking about, were not. In this paper, we will also compare the power spectrum of curvature perturbation, in its Jordan frame, to the PLANCK data. Our numerical plot shows that it is very easy to make the theoretical results consistent with the observational data.

The present paper is organized as follows. Section II gives the background of our model. We transfer the model into Einstein frame and solve the equation of motion to get the inflationary 