Primordial gravitational waves and the H-0-tension problem

We analyze the H-0-tension problem in the context of models of the early universe that predict a blue tilted spectrum of primordial gravitational waves (GWs), which is a positive value of the tensor tilt n(T). By considering the GW's contribution, N-eff(GW), to the effective number of relativistic degrees of freedom, N-eff, and assuming standard particle physics, we discuss the effects of N-eff(GW) on the background expansion, especially the constraints on the Hubble parameter H-0. We analyze three scenarios that take into account the contribution of N-eff(GW) using recent data of cosmic microwave background, baryon acoustic oscillation, the latest measurement of the local expansion rate, along with the LIGO constraints on the tensor to scalar ratio, r, and the tensor index. For the models explored, we show that an additional contribution from the primordial GW's background to N-eff does not solve but alleviates the current H-0-tension problem.