Constraining Axion Dark Matter with Big Bang Nucleosynthesis
  We show that Big Bang Nucleosynthesis (BBN) significantly constrains
axion-like dark matter. The axion acts like an oscillating QCD $\theta$ angle
that redshifts in the early universe, increasing the neutron-proton mass
difference at neutron freeze-out. An axion-like particle that couples too
strongly to QCD results in the underproduction of 4He during BBN and is thus
excluded. The BBN bound overlaps with much of the parameter space that would be
covered by proposed searches for time-varying neutron EDMs. The QCD axion does
not couple strongly enough to affect BBN.
