slow-roll parameters. Therefore, although it is difficult to integrate (\[TrsandTss\]) numerically, it is convenient to assume that the coefficients $A$ and $B$ in Eq. (\[eqlargescale\]) are nearly constants, so one simply have: T\_[[R]{}[S]{}]{}(e\^[BN\_]{}-1) , T\_[[S]{}[S]{}]{}e\^[BN\_]{} , where $N_\ast$ denotes the efolding number from Hubble-crossing time to the end of inflation. Taking this into account, one can straightforwardly get the final power spectrum of curvature perturbation in the original Jordan frame, namely $\tilde{\cal R}$, as: \[scalarspectrumJF\] \_=[C]{} . where =1+\^2 , and from Eq. (\[index2\]) one can get the spectral index in Jordan frame as: \[indexJF\] \_[R]{}&=&1-2\_-2\_-+ . From Eqs. (\[scalarspectrumJF\]) we can see that, when ${\cal C}=1$, $\tilde{\cal P}_{\tilde{\cal R}}$ will coincide with ${\cal P}_{{\cal R}}$, so ${\cal C}$ will behave as an estimator of the inequality between curvature perturbations in Einstein and Jordan frame in our model. From the expressions of $n_{\cal R}$ in Eq. (\[indexJF\]), one could get nontrivial constraints on slow-roll parameters, which will be different from what is done in Einstein frame. The difference comes from two sources, one is due to the frame transformation, and the other is caused by the deviation of ${\cal C}$ from 1, namely the inequality of the perturbations in two 