frames.

How can we physically understand the possibility that the isocurvature modes do not decay to zero at the end of inflation? If that happens, it will indicate that there are still different components when inflation ends, namely the d.o.f.s in inflation may decay into different products. An example is that in m.d.o.f. systems, the dominant d.o.f. decays into radiation, while the subdominant ones decay into baryons, cold dark matter or neutrinos. As long as there has more than one component at the end of inflation, remnant isocurvature perturbations will appear, and according to Eq. (\[differenceR\]), the frame difference of the adiabatic ones will show up. The newest PLANCK paper has carefully discussed these cases, and showed us the primordial isocurvature fractions $\beta_{iso}\equiv{\cal P}_{\cal S}/({\cal P}_{\cal R}+{\cal P}_{\cal S})$ in various cases by numerical study [@Ade:2013lta]. In the most general case, the $95\%$ upper limit of the primordial isocurvature fractions is $\beta_{iso}<0.6$, while in our models, for example when $T_{{\cal S}{\cal S}}$ takes the value $0.9$, one could get $\beta_{iso}\sim 0.4$, well within the allowed range. On the other hand however, the total vanish of the isocurvature modes means that the frame difference will disappear again at the end of 