Collapse of Axion Domain Wall Induced by Helical Primordial Magnetic Fields

Abstract

Stable domain wall (DW) must decay to avoid overclose the Universe. A commonly used solution is to slightly break the PQ symmetry by introducing a bias term in the potential. In this work, we propose an alternative, symmetry-preserving mechanism: coupling the axion field to a helical primordial magnetic field (PMF) via the Chern-Simons term. Using three-dimensional lattice simulations, we evolve the DW network and demonstrate that it can successfully drive DW decay. Our quantitative results further show that the correlation length of the PMF plays a crucial role in determining the decay rate of the DW network and the resulting axion and gravitational wave radiation.

Figures (14)

• Figure 1: The results of scaling parameter $\mathcal{A}$. The top panel shows the cases with the fixed $\sigma_M=1$. The value at the tail of each curve in the first figure indicates the corresponding $\lambda_B H_i$ associated with that case. The black curve corresponds the case $\alpha=0$. The bottom panel shows the cases the fixed $\lambda_B\sim0.2H^{-1}_i$.
• Figure 2: The parameter space of $f_a$ and $\lambda_B$. We choose $C=C_0$ and different $m_a$. The shaded region represents the forbidden region $\Omega_{a}>\Omega_{DM}$.
• Figure 3: The GW spectra at $\tau = 11$ are shown. The unphysical high-frequency region corresponding to scales smaller than the DW width (with $k > m$) has been removed.
• Figure 4: Detectability of the GW spectra for $\lambda_B$ cases. We use $f_a=5\times10^{16}\text{GeV}$ . The sensitivity curves of LISA gw_LISA_1gw_LISA_2, TianQin gw_TianQin_1gw_TianQin_2, Taiji gw_TaiJi_1gw_TaiJi_2, $\mu$Ares gw_muAres_1, DECIGO gw_DECIGO_1gw_DECIGO_2gw_DECIGO_3gw_DECIGO_4, BBO gw_BBO_1gw_BBO_2gw_BBO_3, SKA gw_SKA_1, NANOGrav gw_NANOGrav_1, PPTA gw_PPTA_1 and EPTA gw_EPTA_1 are presented.
• Figure 5: The effective potential defined by Eq. \ref{['eq:eff_potential']}. We use different $\langle F_{\mu\nu}\tilde{F}^{\mu\nu}\rangle$ to show the influence of CS term.