Gravitational Waves and Dark Radiation from Dark Phase Transition:
  Connecting NANOGrav Pulsar Timing Data and Hubble Tension
  Recent pulsar timing data reported by the NANOGrav collaboration may indicate
the existence of a stochastic gravitational wave background around $f \sim
10^{-8}$ Hz. We explore a possibility to generate such low-frequency
gravitational waves from a dark sector phase transition. Assuming that the dark
sector is completely decoupled from the visible sector except via the
gravitational interaction, we find that some amount of dark radiation should
remain until present. The NANOGrav data implies that the amount of dark
radiation is close to the current upper bound, which may help mitigate the
so-called Hubble tension. If the existence of dark radiation is not confirmed
in the future CMB-S4 experiment, it would imply the existence of new particles
feebly interacting with the standard model sector at an energy scale of
O(1-100) MeV.
