Axion dark matter in the post-inflationary Peccei-Quinn symmetry breaking scenario

We consider extensions of the Standard Model in which a spontaneously broken global chiral Peccei-Quinn (PQ) symmetry arises as an accidental symmetry of an exact $Z_N$ symmetry. For $N=9$ or 10, this symmetry can protect the accion—the Nambu-Goldstone boson arising from the spontaneous breaking of the accidental PQ symmetry—against semiclassical gravity effects, thus suppressing gravitational corrections to the effective potential, while it can at the same time provide for the small explicit symmetry breaking term needed to make models with domain wall number $N_{\mathrm{DW}}>1$, such as the popular Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model ($N_{\mathrm{DW}}=6$), cosmologically viable even in the case where spontaneous PQ symmetry breaking occurred after inflation. We find that $N=10$ DFSZ accions with mass $m_A\approx 3.5–4.2\mathrm{meV}$ can account for cold dark matter and simultaneously explain the hints for anomalous cooling of white dwarfs. The proposed helioscope International Axion Observatory—being sensitive to solar DFSZ accions with mass above a few meV—will decisively test this scenario.

Figure 1

Plot of the observational constraints on the parameter space of $(f_A,|g|)$ in the DFSZ accion models for the assumption of exact scaling [panel (a)] and that of deviation from scaling [panel (b)]. Here, we take $N=9$ for the discrete symmetry and $N_{\mathrm{DW}}=6$ for the domain wall number. The region below the blue or cyan lines is excluded since the accion abundance exceeds the observed cold dark matter abundance ${\mathrm{\Omega }}_{\mathrm{CDM}}{h}^2\simeq 0.12$. On the blue (cyan) lines, the lifetime of the domain walls are estimated based on the criterion that the area density of the walls becomes smaller than 10% (1%) of that with $\mathrm{\Xi }=0$. The dotted blue (cyan) lines represent uncertainties of the estimation of the relic accion abundance. In the red region, the condition given by Eq. (2.20) is violated, and the Planck-suppressed operator dominates over the QCD potential for the accion field. The yellow lines correspond to the bound from the $CP$ violation [Eq. (2.19)] for ${\mathrm{\Delta }}_D=1$, $10^{-4}$, and $10^{-8}$. The region above these lines is also excluded according to the value of ${\mathrm{\Delta }}_D$.

Figure 2

The same figure as Fig. 1, but observational constraints are plotted for the DFSZ accion models with $N=10$ based on (a) the assumption of exact scaling and (b) that of deviation from scaling.

Figure 3

Astrophysical and cosmological constraints on the accion decay constant $f_A$ or the accion mass $m_A$. The colored intervals represent the bounds obtained by the cold dark matter overproduction in the KSVZ models (red), WDLFs (magenta), RGs (purple), SN1987A (green), and HBs (brown). In the DFSZ models, the region enclosed by the dashed lines is also excluded because of the cold dark matter overproduction. The orange arrows represent the mass range favored by WDLFs [Eq. (4.7)]. The red arrow represents the predicted mass range, where accions explain the observed cold dark matter abundance in the KSVZ models, while the gray and blue arrows represent that in the DFSZ models with $N=9$ and $N=10$, respectively. The deep gray (blue) line corresponds to the prediction obtained for the case with $|g|=1$ and a minimal tuning of ${\mathrm{\Delta }}_D$, while the light gray (blue) line corresponds to that allowed for the case with $|g|<1$ and/or a further tuning of ${\mathrm{\Delta }}_D$ in the $N=9$ (10) DFSZ models.

Figure 4

Sensitivities to the accion-photon coupling $g_{A\gamma }$ of ongoing and planned detectors and predictions of accion dark matter models (adapted from Ref. [81]). The yellow region corresponds to the generic prediction for the QCD axion models. Colored thick lines represent the parameter range in which accions explain the observed cold dark matter abundance for KSVZ I (red), KSVZ II (brown), KSVZ III (orange), DFSZ I with $N=9$ and $|g|=1$ (gray), DFSZ I with $N=10$ and $|g|=1$ (blue), DFSZ II with $N=9$ and $|g|=1$ (magenta), and DFSZ II with $N=10$ and $|g|=1$ (purple). For DFSZ models, the observed dark matter abundance can also be explained in the parameter range represented by the dotted lines if we allow smaller values of $|g|<1$ and/or a further tuning of the phase parameter ${\mathrm{\Delta }}_D$.