Evolution of axions in the presence of primordial magnetic fields
  We study the evolution of axions interacting with primordial magnetic fields
(PMFs) starting just from the QCD phase transition in the expanding universe.
This interaction is owing to the Primakoff effect. Adopting the zero mode
approximation for axions, we derive the system of equations for axions and
magnetic fields, where the expansion of the universe and the spectra of
magnetic fields are accounted for exactly. We find that the contribution of the
Primakoff effect to the dynamics of axions and magnetic fields is rather weak.
It confirms some previous estimates leading to analogous conclusions, when
accounting here for the Hubble expansion both for an uniform axion field and
non-uniform PMFs using Fourier spectra for their energy and helicity densities.
We solve the corresponding system of the evolution equations and find that the
axion zero mode, when evolving during radiation era, has its amplitude at the
level sufficient for that axion to be a good candidate for the cold dark
matter.
