Primordial gravitational waves and the H0-tension problem
  We analyse the H0-tension problem in the context of models of the early
universe that predict a blue tilted spectrum of primordial gravitational waves
(GW's). By considering the GW's contribution, Neff^GW, to the effective number
of relativistic degrees of freedom, Neff, and assuming standard particle
physics, we discuss the effects of Neff^GW on the background expansion,
especially the constraints on the Hubble parameter H0. We analyse three
scenarios which take into account the contribution of Neff^GW and perform a
statistical study 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 and the tensor index.
For the models explored, we show that an additional contribution from the
primordial GW's background to Neff does not solve but alleviate the current
H0-tension problem.
