A Revision to the Issue of Frames by Non-minimal Large Field Inflation

We present an extended study of inflationary models that inflaton field is non-minimally coupled with gravity. We study parameters space of the models up to the second (and in some cases third) order of the slow-roll parameters for usual large field potentials in Jordan and Einstein frames that are connected each other by conformal transformation. We calculate inflationary parameters and the results are compared in both frames and also with observations. By using the recent observational datasets, we present a discussion in order to clarify the physical frame between Jordan and Einstein frames. Also, some suggestions are expressed in order to navigate us for the future works.