Late-Time Magnetogenesis Driven by Axionlike Particle Dark Matter and a Dark Photon

We propose a mechanism generating primordial magnetic fields after the $e^{+}{e}^{-}$ annihilations. Our mechanism involves an ultralight axionlike particle (ALP) which constitutes the dark matter and a dark $U(1{)}_X$ gauge boson introduced to bypass the obstacle placed by the conductivity of cosmic plasma. In our scheme, a coherently oscillating ALP amplifies the dark photon field, and part of the amplified dark photon field is concurrently converted to the ordinary magnetic field through the ALP-induced magnetic mixing. For the relevant ALP mass range ${10}^{-21}\mathrm{eV}\lesssim m_{\varphi }\lesssim {10}^{-17}\mathrm{eV}$, our mechanism can generate $B\sim {10}^{-24}\mathrm{G}(m_{\varphi }/{10}^{-17}\mathrm{eV}{)}^{5/4}$ with a coherent length $\lambda \sim (m_{\varphi }/{10}^{-17}\mathrm{eV}{)}^{-1/2}\mathrm{kpc}$, which is large enough to provide a seed of the galactic magnetic fields. The mechanism also predicts a dark $U(1{)}_X$ electromagnetic field $E_X\sim B_X\sim 80\mathrm{nG}(m_{\varphi }/{10}^{-17}\mathrm{eV}{)}^{-1/4}$, which can result in interesting astrophysical or cosmological phenomena by inducing the mixings between the ALP, ordinary photon, and dark photon states.

Figure 1

The time evolution of $r$ (top), $\epsilon$ (middle), and $b$ (bottom) from the lattice calculation with the number of grid $128^3$. One can also see $a_X/a_{\mathrm{osc}}\simeq 5$ from the epoch when $\epsilon$ and $b$ almost saturate. Note that two different simulation boxes with comoving side lengths $L=2{\tau }_{\mathrm{osc}}$ (red solid) and $L=0.5{\tau }_{\mathrm{osc}}$ (blue dotted) show consistent results.

Figure 2

The power spectrum of produced magnetic fields from the lattice calculation at $a/a_{\mathrm{osc}}=30$. Setup is the same as in Fig. 1. Results from different simulation boxes are consistent around the spectral peak.