Cosmological axion and a quark nugget dark matter model

We study a dark matter (DM) model offering a very natural explanation of two (naively unrelated) problems in cosmology: the observed relation ${\mathrm{\Omega }}_{\mathrm{DM}}\sim {\mathrm{\Omega }}_{\text{visible}}$ and the observed asymmetry between matter and antimatter in the Universe, known as the “baryogenesis” problem. In this framework, both types of matter (dark and visible) have the same QCD origin, form at the same QCD epoch, and are proportional to one and the same dimensional parameter of the system, ${\mathrm{\Lambda }}_{\mathrm{QCD}}$, which explains how these two naively distinct problems could be intimately related, and could be solved simultaneously within the same framework. More specifically, the DM in this model is composed by two different ingredients: the (well-studied) DM axions and the (less-studied) quark nuggets made of matter or antimatter. We focus on the quantitative analysis of the relation between these two distinct components contributing to the dark sector of the theory determined by ${\mathrm{\Omega }}_{\mathrm{DM}}\equiv [{\mathrm{\Omega }}_{\mathrm{DM}}(\text{nuggets})+{\mathrm{\Omega }}_{\mathrm{DM}}(\text{axion})]$. We argue that the nuggets’ DM component always traces the visible matter density, i.e., ${\mathrm{\Omega }}_{\mathrm{DM}}(\text{nuggets})\sim {\mathrm{\Omega }}_{\text{visible}}$, and this feature is not sensitive to the parameters of the system such as the axion mass $m_a$ or the misalignment angle ${\theta }_0$. It should be contrasted with conventional axion production mechanisms due to the misalignment when ${\mathrm{\Omega }}_{\mathrm{DM}}(\text{axion})$ is highly sensitive to the axion mass $m_a$ and the initial misalignment angle ${\theta }_0$. We also discuss the constraints on this model related to the inflationary scale $H_I$, nonobservation of the isocurvature perturbations and the tensor modes. We also comment on some constraints related to various axion search experiments.

Figure 1

This diagram illustrates the interrelation between the axion production due to the misalignment mechanism and the nuggets’ formation which starts before the axion field $\theta$ relaxes to zero. Possible cooling paths are denoted as path 1, 2 or 3. The phase diagram is in fact much more complicated as the dependence on the third essential parameter, the $\theta$ is not shown as it is largely unknown. It is assumed that the initial axion field starts at ${\theta }_0$, while the nuggets complete their formation in the CS region at $T_{\text{form}}\approx 41\mathrm{MeV}$, $\mu >{\mu }_c$ and $\theta \approx 0$.

Figure 2

Contour plots of $c$ as a function of $m_a$ and $B$ for (a) ${\theta }_{a,i}=10^{-3}$ and (b) ${\theta }_{a,i}=10^0$, respectively, with the fixed values $H_I/2\pi =5.7\times {10}^8\mathrm{GeV}$ and $\kappa ={10}^{-4}$. Different colors (shown on the right) correspond to the different values of the parameter $c\sim 1$. Precisely this parameter $c$ essentially determines the relation between dark and visible matter according to approximate relation (4). Here $B$ corresponds to the baryon number of an antinugget (which is also the case for other figures in this subsection).

Figure 3

Contour plots of $c$ as a function of $m_a$ and $B$ for (a) $H_I/2\pi ={10}^{10}\mathrm{GeV}$ and (b) $H_I/2\pi =10^{11}\mathrm{GeV}$, respectively, with the fixed value ${\theta }_{a,i}={10}^{-1}$ and $\kappa ={10}^{-4}$. Different colors (shown on the right) correspond to the different values of the parameter $c\sim 1$.

Figure 4

Model 2. Contour plots of $c$ as a function of $m_a$ and $B$ for specific values of $H_I$, ${\theta }_{a,i}$, and $\kappa ={10}^{-4}$. (a) $(M_q,\mu )=(200,400)\mathrm{MeV}$. (b) $(M_q,\mu )=(160,500)\mathrm{MeV}$. Different colors (shown on the right) correspond to the different values of the parameter $c\sim 1$.

Figure 5

Contour plots of ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_{\mathrm{DM}}$ as a function of $m_a$ and $\varphi =\sqrt{{\theta }_{a,i}^2+{(H_I/(2\pi f_a))}^2}$. Different colors (shown on the left) correspond to the different values of ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_{\mathrm{DM}}$.

Figure 6

Contour plots of ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_{\mathrm{DM}}$ as a function of $c$ and ${\kappa }^{-1}{B}^{1/3}{m}_a$. Different colors (shown on the right) correspond to the different values of ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_{\mathrm{DM}}$.

Figure 7

Plot of $3{\epsilon }_{\mathrm{tot}}/m_p$ vs ${\kappa }^{-1}{B}^{1/3}{m}_a/m_{\pi }$.

Figure 8

Plot of $3{\epsilon }_{\mathrm{QCD}}/m_p$ vs ${\kappa }^{-1}{B}^{1/3}{m}_a/m_{\pi }$.

Figure 9

Plot of ${\epsilon }_{\mathrm{DW}}/{\epsilon }_{\mathrm{tot}}$ vs ${\kappa }^{-1}{B}^{1/3}{m}_a/m_{\pi }$.