Gravitational Waves from Post-Inflationary Magnetism: Direct and Scalar-Induced Contributions

We study stochastic gravitational waves generated in a post-inflationary magnetogenesis scenario with time-dependent gauge couplings during inflation and reheating. In this setup, magnetic anisotropic stress directly sources gravitational waves, while the induced curvature perturbations generate an additional scalar-induced GW component. We compare the spectral behavior of the two contributions and find that the magnetic component dominates the peak amplitude, whereas the scalar-induced contribution becomes important on larger scales. For blue magnetic spectra with $n_{\rm b}\geq3/2$, both spectra follow the universal infrared scaling $\Omega_{\rm GW}(f\ll f_{\rm peak})\propto f^3$. However, their ultraviolet behaviors differ significantly for $f>f_{\rm peak}$, leading to distinct spectral features. For suitable reheating and magnetogenesis parameters, the resulting GW signal naturally extends into the nano-Hz range relevant for pulsar timing array observations, while remaining consistent with current bounds. The distinct spectral features of the two components may provide a useful probe of reheating dynamics and primordial magnetogenesis.