In the measurements of cosmic microwave background polarizations , three frequency channels are necessary for discriminating the primordial B-modes from the polarized dust and the synchrotron emission .
We carry out an optimistic estimate on the sensitivity to the detection of primordial gravitational waves using the cosmic microwave background B-modes only , and explore how to reach the thresholds for the tensor-to-scalar ratio r in the theoretically well-motivated inflation models .
For example , Lyth bound implies r \simeq 2 \times 10 ^ { -3 } , a corrected Lyth bound shows r \simeq 7 \times 10 ^ { -4 } , and some typical inflation models gives r \simeq 4 \times 10 ^ { -5 } .
Taking into account the up-to-date constraints on r , i.e . r _ { 0.05 } < 0.07 at 95 \% confidence , we find that the consistency relation n _ { t } = - r / 8 in the canonical single-field slow-roll inflation can not be distinguished from the scale invariance , due to the cosmic variance in the power spectrum of cosmic microwave background B-modes .
The cosmic variance places an inevitable limit on the measurements of the tensor spectral index , i.e . \sigma _ { n _ { t } } \simeq 0.01 for 2 \leqslant \ell \leqslant \ell _ { \text { max } } = 300 .