Axion quark nugget dark matter model: Size distribution and survival pattern

We consider the formation and evolution of axion quark nugget (AQN) dark matter particles in the early Universe. The goal of this work is to estimate the mass distribution of these objects and assess their ability to form and survive to the present day. We argue that this model allows a broad range of parameter space in which the AQN may account for the observed dark matter mass density, naturally explains a similarity between the “dark” and “visible” components, i.e., ${\mathrm{\Omega }}_{\text{dark}}\sim {\mathrm{\Omega }}_{\text{visible}}$, and also offers an explanation for a number of other long-standing puzzles, such as the “primordial lithium puzzle” and “the solar corona mystery,” among many other cosmological puzzles.

Figure 1

This diagram illustrates the interrelation between axion production due to the misalignment mechanism and the nuggets’ formation which starts before the axion field $\theta$ relaxes to zero. Adopted from Ref. [9].

Figure 2

Numerical results for the nugget evolution. The two solid blue lines represent the upper and lower envelope of $R$ oscillations, respectively. The shaded light blue region represents the numerous oscillations. The solid orange line represents the lower envelope of $\mu$ oscillations (we do not show the upper envelope and the shaded region for $\mu$ oscillations to make the picture more clear). The dashed blue and orange lines represent $R_{\mathrm{form}}$ and ${\mu }_{\mathrm{form}}$ using simple analytical arguments as expressed by Eqs. (a8) and (a9), respectively. We see that they match the numerical results for the nugget evolution pretty well.

Figure 3

Parameter space of $R_0$ and $T_0$. The colored region represents the initially allowed ($R_0$, $T_0$) values for the formation of closed domain walls. Different colors represent different magnitudes of $f(R_0,T_0)$ which decreases from the light yellow part to the deep blue part [gradually away from the correlation length $\xi (T_0)$]. The green lines are the contour lines of $B$, i.e., each line corresponds to the same value of $B$, with $B$ increasing from left to right.

Figure 4

The relation between $dN/dB$ and $b\equiv B/B_{\min }$. We choose $\tau =2$, $\lambda =10$, and $\beta =3.925$ for both panels. The difference between panels (a) and (b) is the value of $\delta$. In panel (a) $\delta \approx -1$ and thus $\alpha =1.2$; in panel (b) we choose $\delta \approx -4$ to make $\alpha =2$. The solid black and dashed green lines in each panel represent Eqs. (b5) and (b8), respectively (the prefactor $N_{0}P/B_{\min }$ in the two equations is rescaled to completely show $dN/dB$ in the range from 0 to 1 for illustrative purposes).