Updated constraints and forecasts on primordial tensor modes

We present new, tight, constraints on the cosmological background of gravitational waves (GWs) using the latest measurements of CMB temperature and polarization anisotropies provided by the Planck, BICEP2 and Keck Array experiments. These constraints are further improved when the GW contribution NeffGW to the effective number of relativistic degrees of freedom Neff is also considered. Parametrizing the tensor spectrum as a power law with tensor-to-scalar ratio r, tilt nₜ and pivot 0.01 Mpc^-1, and assuming a minimum value of $r=0.001$, we find $r<0.089$, nₜ=1.7_-2.0+2.1 (95% CL, no NeffGW) and $r<0.082$, nₜ=-0.05_-0.87+0.58 (95% CL, with NeffGW). When the recently released 95 GHz data from Keck Array are added to the analysis, the constraints on r are improved to $r<0.067$ (95% CL, no NeffGW), $r<0.061$ (95% CL, with NeffGW). We discuss the limits coming from direct detection experiments such as LIGO-Virgo, pulsar timing (European Pulsar Timing Array) and CMB spectral distortions (FIRAS). Finally, we show future constraints achievable from a COrE-like mission: if the tensor-to-scalar ratio is of order 10^-2 and the inflationary consistency relation nₜ=-r/8 holds, COrE will be able to constrain nₜ with an error of 0.16 at 95% CL. In the case that lensing B-modes can be subtracted to 10% of their power, a feasible goal for COrE, these limits will be improved to 0.11 at (95% CL).