(black solid), $(10^4,1.8)$ (red dash), $(0.1,1.5)$ (blue dot dash) respectively. The power spectrum information $(A_s, n_s, r)$ are obtained as $(2.13\times10^{-9},0.9627,5.56\times10^{-3})$ (black solid), $(2.15\times10^{-9},0.9708,2.60\times10^{-2})$ (red dash), $(2.19\times10^{-9},0.9609,0.11)$ (blue dot dash). Lower panel: the $f(\tilde R)=\tilde R+\xi \tilde R^2$ case, where we choose $\xi$ as $1/6$ (black solid), $100$ (red dash), $1000$ (blue dot dash) respectively. The power spectrum information $(A_s, n_s, r)$ are obtained as $(2.17\times10^{-9},0.9629,2.73\times10^{-3})$ (black solid), $(2.21\times10^{-9},0.9703,1.55\times10^{-2})$ (red dash), $(2.27\times10^{-9},0.9645,1.28\times10^{-2})$ (blue dot dash).[]{data-label="tt"}](tt2.eps)

conclusion
==========

In this paper we discussed about a well-motivated subclass of inflationary models, namely a scalar field in $f(R)$ modified gravity, and calculate the perturbations generated from this model. As a system of m.d.o.f., it is convenient to transform it into Einstein frame so that it becomes a minimal-coupling two-field system, the perturbations of which can be calculated in a standard way. However, contrary to the cases of pure $f(R)$ modified gravity or single field models nonminimally coupled to gravity in which the curvature perturbations in Jordan and Einstein frames are equivalent, in our model they are different. Therefore, one should “pull-back" the Einstein-frame results via the conformal transformations in order to take the “real" results of perturbations in the Jordan frame. In this 