Improved constraints on primordial gravitational waves in light of the H0 tension and BICEP/Keck data

The H0 tension that the standard ACDM model is suffering from can be resolved with prerecombination early dark energy. We present the first constraint on the tensor-to-scalar ratio r in corresponding H0-tension -free cosmologies using the most recent BICEP/Keck cosmic microwave background (CMB) B-mode polarization data. We find, combining BICEP/Keck with Planck18 CMB and baryon acoustic oscillation data, that the models with larger Hubble-Lemaitre-constant H0 will have tighter upper bound on r, and resolution of the H0 tension (H0 -73 km/s/Mpc) tightens the upper bound to r < 0.028(95% C.L.), 25% tighter than the ACDM constraint r < 0.036. We clarify the origin of this tightened bound.