  Minuscule primordial black holes before the end and after inflation can serve
as "time capsules" bringing back energy from the past to a later epoch when
they evaporate. As these black holes behave like matter, while the rest of the
Universe content behaves like radiation, the mass fraction of these black
holes, that is tiny at formation, becomes significant later. If sufficiently
small, these black holes will evaporate while the Universe is still radiation
dominated. We revisit this process and point out that gravitons produced during
the evaporation behave as ``dark radiation". If the initial black holes are
uniformly distributed so will be the gravitons and in this case they will be
free of Silk damping and avoid current limits on "dark radiation" scenarios.
Seeds for such black holes can arise during the last phases of inflation. We
show here that with suitable parameters, this background graviton field can
resolve the Hubble tension. We present current observational constraints on
this scenario and suggest upcoming observational tests to prove or refute it.
Finally, we also elaborate on the graviton background produced by particle
annihilation during the Planck era or shortly after inflation.
