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 thePlanck, BICEP2 andKeck Arrayexperiments. These constraints are further improved when the GWcontributionNGWeffto the effective number of relativistic degrees of freedomNeffis also considered.Parametrizing the tensor spectrum as a power law with tensor-to-scalar ratior, tiltntand pivot0.01 Mpc−1, and assuming a minimum value ofr= 0.001, we findr <0.089,nt= 1.7+2.1−2.0(95% CL,noNGWeff) andr <0.082,nt=−0.05+0.58−0.87(95% CL, withNGWeff). When the recently released 95 GHzdata fromKeck Arrayare added to the analysis, the constraints onrare improved tor <0.067(95% CL, noNGWeff),r <0.061 (95% CL, withNGWeff). We discuss the limits coming from directdetection experiments such as LIGO-Virgo, pulsar timing (European Pulsar Timing Array) andCMB spectral distortions (FIRAS). Finally, we show future constraints achievable from a COrE-like mission: if the tensor-to-scalar ratio is of order 10−2and the inflationary consistency relationnt=−r/8 holds, COrE will be able to constrainntwith an error of 0.16 at 95% CL. In the casethat lensingB-modes can be subtracted to 10% of their power, a feasible goal for COrE, these limitswill be improved to 0.11 at (95% CL