We study the evolution of photon polarization during the photon-axion conversion process with focusing on the magnetic field configuration dependence. Most previous studies have been carried out in a conventional model where a network of magnetic domains is considered and each domain has a constant magnetic field. We investigate a more general model where a network of domains is still assumed, but each domain has a helical magnetic field. We find that the asymptotic behavior does not depend on the configuration of magnetic fields. Remarkably, we analytically obtain the asymptotic values of the variance of polarization in the conventional model. When the helicity is small, we show that there appears the damped oscillating behavior in the early stage of evolution.Moreover, we see that the constraints on the axion coupling and the cosmological magnetic fields using polarization observations are affected by the magnetic field configuration. This is because the different transient behavior of polarization dynamics is caused by the different magnetic field configuration. Recently, [C. Wang and D. Lai, J. Cosmol. Astropart. Phys. 06 (2016) 006.] claimed that the photon-axion conversion in helical model behaves peculiarly. However, our helical model gives much closer predictions to the conventional discontinuous magnetic field configuration model.

It is known that a coherently oscillating axion field is a candidate of the dark matter. In the presence of the oscillating axion, the photon can be resonantly produced through the parametric amplification. In the universe, there also exist cosmological magnetic fields which are coherent electromagnetic fields. In the presence of magnetic fields, an axion can be converted into a photon, and vice versa. Thus, it is interesting to investigate what happens for the axion-photon system in the presence of both the axion dark matter and the magnetic fields. This system can be regarded as a coupled system of the axion and the photon whose equations contain the Mathieu type terms.We find that the instability condition is changed in the presence of magnetic fields in contrast to the conventional Mathieu equation. The positions of bifurcation points between stable and unstable are shifted and new instability bands appear. This is because the resonantly amplified axion can be converted to photon, and vice versa.

It is well known that gravitons can convert into photons, and vice versa, in the presence of cosmological magnetic fields. We study this conversion process in the context of the atomic dark matter scenario. In this scenario, we can expect cosmological dark magnetic fields, which are free from the stringent constraint from the cosmic microwave observations. We find that gravitons can effectively convert into dark photons in the presence of cosmological dark magnetic fields.The graviton-dark photon conversion effect may open up a new window for ultrahigh frequency gravitational waves.