Cosmological abundance of the QCD axion coupled to hidden photons
  We study the cosmological evolution of the QCD axion coupled to hidden
photons. For a moderately strong coupling, the motion of the axion field leads
to an explosive production of hidden photons by tachyonic instability. We use
lattice simulations to evaluate the cosmological abundance of the QCD axion. In
doing so, we incorporate the backreaction of the produced hidden photons on the
axion dynamics, which becomes significant in the non-linear regime. We find
that the axion abundance is suppressed by at most ${\cal O}(10^{2})$ for the
decay constant $f_a = 10^{16}$ GeV, compared to the case without the coupling.
For a sufficiently large coupling, the motion of the QCD axion becomes strongly
damped, and as a result, the axion abundance is enhanced. Our results show that
the cosmological upper bound on the axion decay constant can be relaxed by a
few hundred for a certain range of the coupling to hidden photons.
