Axion propagation in a gravitational wave background

Axion-like particles provide a natural bridge between hidden-sector physics, dark matter, and symmetry principles beyond the Standard Model. They arise in theories with spontaneously broken global symmetries and interact with electromagnetism through the pseudoscalar invariant $aF_{\mu\nu}\tilde F^{\mu\nu}$. This coupling links axion dynamics to the electromagnetic parity-odd invariant $E\cdot B$, making axion electrodynamics a useful framework for studying how symmetry structures are modified by external fields. We investigate how weak gravitational wave backgrounds affect axion--photon dynamics in compact-object environments without introducing new fundamental interactions.

Starting from the covariant axion-photon effective action, we derive the coupled evolution equations governing the axion and electromagnetic sectors in the presence of an external perturbative background. We then specialize the system to the case of a weak excitation propagating along the $z$ direction and analyze the resulting modifications of the axion-photon interaction terms. The equations are expanded to leading order in the perturbation amplitude, and a reduced one-dimensional model is constructed to isolate the role of the pseudoscalar source term $E_iB^i$ in the coupled dynamics.

The external perturbation induces time-dependent corrections to the axion evolution operator and generates modifications of the electromagnetic sector. For a strictly one-dimensional axion configuration, $a=a(t,z)$, the leading-order correction to the axion propagation operator cancels identically. Nevertheless, axion dynamics remain sensitive to the perturbed environment through the electromagnetic fields, whose evolution modulates the pseudoscalar interaction term $E_iB^i$.

These results show that axion--photon interactions can develop coherent, time-dependent features driven by external perturbations through the standard pseudoscalar coupling alone. The analysis provides a framework for investigating axion dynamics in realistic high-energy and astrophysical environments, and clarifies how anisotropic perturbations can influence axion propagation, axion-photon conversion, and the generation of electromagnetic signals.