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Current and future B-mode polarization data are the most powerful observablesto constrain gravitational waves from the early Universe. We set conservativeconstraints on tensor modes when relaxing the inflationary consistencycondition $n_t=-r/8$ between the tensor tilt $n_t$ and the tensor-to-scalarratio r. By adding a power-law spectrum of tensor perturbations to$\Lambda$CDM, and parameterizing this tensor contribution by two independentprimordial tensor-to-scalar ratios $(r_1,r_2)$ at $k_1 = 0.005$ Mpc$^{-1}$ and$k_2 = 0.02$ Mpc$^{-1}$, Planck and BICEP/Keck Array 2018 data (BK18) lead toconstraints $r_{0.005} < 0.030$ and $r_{0.02} < 0.098$ at 95% CL. Thecorresponding upper bound $r_{0.01} < 0.039$ is by a factor of 2 tighter thanthe one obtained with Planck 2018 and the older BK15 data. We then study theperspectives for future CMB experiments that will measure both the reionizationbump and recombination peak of the B-mode polarization angular power spectrum,such as LiteBIRD. We test the robustness of the results to the choice of thescales for $(r_1,r_2)$ in these future perspectives. Whereas distinguishing$n_t=-r/8$ from exact scale invariance is impossible as expected, we show howradical, theoretically motivated departures from $n_t=-r/8$, which areconsistent with the current data, could be distinguished with LiteBIRD.Moreover, LiteBIRD will be able to shrink the allowed parameter space area inthe $(r_{0.005},r_{0.02})$ plane to less than one hundredth of the currentlyallowed area by Planck 2018 and BK18.

Planck and BICEP/Keck Array 2018 constraints on primordial gravitational waves and perspectives for future B-mode polarization measurements