Forecasting sensitivity on tilt of power spectrum of primordial gravitational waves after Planck satellite

By taking into account the contamination of foreground radiations, we employ the Fisher matrix to forecast the future sensitivity on the tilt of power spectrum of primordial tensor perturbations for several ground-based (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G), balloon-borne (EBEX, Spider) and satellite (CMBPol, COrE, LiteBIRD) experiments of B-mode polarizations. For the fiducial model $n_t=0$, our results show that the satellite experiments give good sensitivity on the tensor tilt $n_t$ to the level ${\sigma }_{n_t}\lesssim 0.1$ for $r\gtrsim 2\times {10}^{-3}$, while the ground-based and balloon-borne experiments give worse sensitivity. By considering the BICEP2/Keck Array and Planck (BKP) constraint on the tensor-to-scalar ratio $r$, we see that it is impossible for these experiments to test the consistency relation $n_t=-r\mathrm{/}8$ in the canonical single-field slow-roll inflation models.