Testing inflationary consistency relations by the potential CMB observations

Testing the so-called consistency relations plays an important role for distinguishing the different classes of inflation models. In this paper, we investigate the possible testing based on the potential observations of the cosmic microwave background (CMB) radiation, including the planned CMBPol mission and the ideal CMB experiment where only the reduced cosmic weak lensing contamination for the B-mode polarization is considered. We find that for the canonical single-field inflation and the phantom inflation, the consistency relations are quite hard to be tested: the testing is possible only if $r>0.14$ for CMBPol mission, and $r>0.06$ for the ideal experiment. However, the situation could become much better for the general Lorentz invariant single-field inflation with large non-gaussian signal and the two-field inflation with strong correlation between the adiabatic and the isocurvature perturbations. We find that for these two classes of inflation the testing is possible if $r\gtrsim 10^{-2}$ or even smaller for both CMB experiments.