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.