Production of dark matter axions from collapse of string-wall systems

Abstract

We analyze the spectrum of axions radiated from collapse of domain walls, which have received less attention in the literature. The evolution of topological defects related to the axion models is investigated by performing field-theoretic lattice simulations. We simulate the whole process of evolution of the defects, including the formation of global strings, the formation of domain walls and the annihilation of the defects due to the tension of walls. The spectrum of radiated axions has a peak at the low frequency, which implies that axions produced by the collapse of domain walls are not highly relativistic. We revisit the relic abundance of cold dark matter axions and find that the contribution from the decay of defects can be comparable with the contribution from strings. This result leads to a more severe upper bound on the axion decay constant.

Figures (8)

• Figure 1: Schematics of the procedure to estimate the power spectrum of radiated axions.
• Figure 2: Visualization of one realization of the simulation. In this figure, we take the box size as $L=15$ and $N=256$, which is smaller than that shown in Table \ref{['tab1']}. Other parameters are fixed so that $\lambda=1.0$, $\zeta=3.0$, $\alpha=2.0$, and $\kappa=0.4$. The white lines correspond to the position of strings, while the blue surfaces correspond to the position of the center of domain walls.
• Figure 3: The distribution of the phase of the scalar field $\theta$ on the two-dimensional slice of the simulation box. In this figure, we used the same data that are used to visualize the result with $\tau = 5.0$ in Fig. \ref{['fig2']}. The value of $\theta$ varies from $-\pi$ (blue) to $\pi$ (red). Domain walls are located around the region on which $\theta$ passes through the value $\pm\pi$, while the green region corresponds to the true vacuum ($\theta=0$). The length scale of the change of $\theta$ is roughly estimated as $\sim m_a^{-1}$, which gives the thickness of domain walls.
• Figure 4: Time evolution of the length parameter $\xi$ (left panel) and the area parameter ${\cal A}$ (right-hand panel) for various values of $\kappa$. Although walls do not exist before the time $\tau_1$, we can show the value of ${\cal A}$ evaluated at the time $\tau<\tau_1$. This is because the value of ${\cal A}$ is calculated from the number of grid points on which the phase of the scalar filed passes the value $\theta=\pi$. In this sense, ${\cal A}$ represents the area of domain walls only after the time $\tau_1$.
• Figure 5: The power spectrum of free axions calculated by using PPSE formula (\ref{['eq3-3-8']}) in the simulations with $\kappa=0.3$. We plot the spectra evaluated at two different times $t_1$ and $t_d$. Note that the result of $P(k,t_1)$ shown here does not contain the numerical factor defined in Eq. (\ref{['eq3-4-4']})