Dark Matter and Dark Energy from the Solution of the Strong $CP$ Problem

The Peccei-Quinn (PQ) solution of the strong $CP$ problem requires the existence of axions, which are viable candidates for dark matter. If the Nambu-Goldstone potential of the PQ model is replaced by a potential $V(|\Phi |)$ admitting a tracker solution, the scalar field $|\Phi |$ can account for dark energy, while the phase of $\Phi$ yields axion dark matter. If $V$ is a supergravity (SUGRA) potential, the model essentially depends on a single parameter, the energy scale $\Lambda$. Once we set $\Lambda \simeq {10}^{10}\mathrm{G}\mathrm{e}\mathrm{V}$ at the quark-hadron transition, $|\Phi |$ naturally passes through values suitable to solve the strong $CP$ problem, later growing to values providing fair amounts of dark matter and dark energy.

Figure 1

Densities of the different components vs the scale factor $a$. Figure 1a magnifies the onset of the oscillation regime. Figure 1b shows the low-$z$ behavior. Figure 1c is a landscape picture of the whole evolution. All abscissas are $\log (a/a_0)$.

Figure 2

Density parameters ${\Omega }_{r,b,\theta ,\varphi }$ (radiation, baryons, DM, DE) vs the scale factor $a$.

Figure 3

Time evolution of DM and baryon fluctuations. The top figure shows DM and baryon fluctuation evolution in this model. The two bottom figures compare DM and baryon fluctuation evolutions in this model (solid curve), $\Lambda \mathrm{C}\mathrm{D}\mathrm{M}$ (dot-dashed line), coupled DE (dashed line).

Figure 4

The onset of coherent axion oscillations at the eve of the quark-hadron transition due to the increase of $m(T,\varphi )$ causes the behaviors of ${\rho }_{\theta ,\mathrm{p}\mathrm{o}\mathrm{t}}$, ${\rho }_{\theta ,\mathrm{k}\mathrm{i}\mathrm{n}}$ (a) and ${\omega }_{\varphi ,\theta }=p_{\varphi ,\theta }/{\rho }_{\varphi ,\theta }$ (b) shown here.

Figure 5

$\varphi$ variations cause a dependence of the effective axion mass on scale factor $a$, which is shown here.