Implications of Gravitational-wave Production from Dark Photon Resonance
  to Pulsar-timing Observations and Effective Number of Relativistic Species
  The coherent oscillation of axionic fields naturally drives copious
production of dark photon particles in the early universe, due to resonance and
tachyonic enhancement. During the process, energy is abruptly transferred from
the former to the latter, sourcing gravitational wave generation. The resulting
gravitational waves are eventually to be observed as stochastic background
today. We report analytical results of this production and connect them to the
recent pulsar-timing results by the NANOGrav collaboration. We show an
available parameter space, around the mass $m_\phi \sim 10^{-13} \, {\rm eV}$
and the decay constant $f_\phi \sim 10^{16} \, {\rm GeV}$ with a dimensionless
coupling of ${\cal O}(1)$, for our mechanism to account for the signal. A
mechanism to avoid the axion over-dominating the universe is a necessary
ingredient of this model, and we discuss a possibility to recover a symmetry
and render the axion massless after the production. We also comment on
potential implications of the required effective number of relativistic species
to the determination of the present Hubble constant.
