Axion cosmology in the presence of nontrivial Nambu-Goldstone modes

Axion cosmology is reexamined taking into account the effect of kinetic pseudo-Nambu-Goldstone modes. When Peccei-Quinn (PQ) symmetry is broken by a chiral U(1) singlet, we find that the effect of the kinetic Nambu-Goldstone mode makes the axion dark matter untenable. When PQ symmetry is extended and is broken by two singlets, we find that axion cosmology works, but there are several differences from the axion cosmology studied in the literature. The differences are (1) an ordinary type of dark matter scaling of $1/{\mathrm{cosmic}\mathrm{scale}\text{factor}}^3$ arising from a modulus field and not from the usual angular field, (2) the mass of the dark matter quantum in the ultralight range $({10}^{-32}–{10}^{-14})\mathrm{eV}$, (3) the emergence of dark energy with a present density of order $(\mathrm{a}\mathrm{few}\mathrm{meV}{)}^4$, consistent with observations, (4) the presence of a long-range spin-dependent force, and (5) slow-roll inflation after PQ symmetry breaking when conformal coupling to gravity is introduced.

Figure 1

Three roots $a>b>c$ of algebraic equation appearing constant $R$ solution (10), where $a$, $b$, and $c$ are denoted by the solid black, dashed orange, and dash-dotted blue curves, respectively. The $k=\sqrt{(a-b)/(a-c)}$ factor in the Jacobi solutions is shown by the dotted black curve, changing from $\sim 1$ around $d=0$ to $\sim 0$ at $d\gg 1$.

Figure 2

Time variation of the acceleration force $2\dot{\chi }{c}_{\theta }/{\chi }^3$ in units of $f_a^2$ for the axion angular field $\theta \sim a/f_a$: 0.1 (solid black), $\sqrt{16/27}$ (dashed orange), 1 (dash-dotted blue), and 5 (dotted black). Time $t$ is scaled by the unit $2/(\sqrt{a-c}{f}_a)$ depending on $d$. The time period average can never be in the required axion mass range of $m_a\approx {10}^{-27}{f}_a$.

Figure 3

Solutions ${\chi }_d/f_a$ of Eq. (44) for a few choices of $e$: plot of the function $f(y)=y^4(y^2-1)-e^2$ for $e=2$ (solid black), 1 (dashed orange), 0.5 (dash-dotted blue), and 0.1 (dotted black).