Altered axion abundance from a dynamical Peccei-Quinn scale

We build a model in which the relic abundance of axions is altered from the standard misalignment mechanism, either increased or decreased, due to the presence of a new light scalar that couples to the radial part of the Peccei-Quinn (PQ) field. The light scalar makes the effective PQ symmetry-breaking scale dynamical, altering the early-time dynamics for the axion and affecting its late-time dark matter abundance. We analyze this new mechanism semianalytically and numerically, showing that we can accommodate both lighter or heavier axion dark matter, compared to the standard treatments. We discuss implications of the model for axion searches and fundamental physics.

Figure 1

A realization of the DPQ model with $m_a={10}^{-4}\mathrm{eV}$, $m_{\chi }={10}^{-8}\mathrm{eV}$, $F=0.1$, and $Y_i={\chi }_i/S=5$. The top panel shows the evolution of the axion ($\theta$) and $\chi$ field compared to the evolution of the standard QCD axion (${\theta }_{\mathrm{std}}$). The lower panel shows the abundance parameter $\xi \equiv \rho /n_{\gamma }$ for the axion (${\xi }_a$), the $\chi$ field (${\xi }_{\chi }$), their sum, and the standard axion (${\xi }_{a,\mathrm{std}}$). The dashed line indicates the analytical prediction ${\xi }_{a,\mathrm{an}}$ from Eq. (35), and the dotted line shows ${\xi }_{\mathrm{DM},\mathrm{obs}}\approx 2.9\mathrm{eV}$, the observed DM abundance. This axion mass can, in particular, be interesting for experimental searches targeting this mass, such as MADMAX. In this instance, a heavier axion is adapted to reproduce the observed DM abundance; the $\chi$ field is not light enough to begin oscillations after the axion, rendering the analytical prediction (dashed line) inaccurate.

Figure 2

A realization of the DPQ model with $m_a={10}^{-6}\mathrm{eV}$, $m_{\chi }=2\times {10}^{-10}\mathrm{eV}$, $F=0.1$, and $Y_i={\chi }_i/S=5$. The top panel shows the evolution of the axion ($\theta$) and $\chi$ field compared to the evolution of the standard QCD axion (${\theta }_{\mathrm{std}}$). The lower panel shows the abundance parameter $\xi \equiv \rho /n_{\gamma }$ for the axion (${\xi }_a$), the $\chi$ field (${\xi }_{\chi }$), their sum, and the standard axion (${\xi }_{a,\mathrm{std}}$). The dashed line indicates the analytical prediction ${\xi }_{a,\mathrm{an}}$ from Eq. (35), and the dotted line shows ${\xi }_{\mathrm{DM},\mathrm{obs}}\approx 2.9\mathrm{eV}$, the observed DM abundance. In this instance, a lighter axion is used to illustrate that the analytical estimate can accurately predict the axion abundance in the DPQ model.

Figure 3

A realization of the IPQ model with $m_a={10}^{-6}\mathrm{eV}$, $m_{\chi }=5\times {10}^{-12}\mathrm{eV}$, $F=0.5$, and $Y_i={\chi }_i/S=6$. The top panel shows the evolution of the axion ($\theta$) and $\chi$ field compared to the evolution of the standard QCD axion (${\theta }_{\mathrm{std}}$). The lower panel shows the abundance parameter $\xi \equiv \rho /n_{\gamma }$ for the axion (${\xi }_a$), the $\chi$ field (${\xi }_{\chi }$), their sum, and the standard axion (${\xi }_{a,\mathrm{std}}$). The dashed line indicates the analytical prediction ${\xi }_{a,\mathrm{an}}$ from Eq. (35), and the dotted line shows ${\xi }_{\mathrm{DM},\mathrm{obs}}\approx 2.9\mathrm{eV}$, the observed DM abundance. This axion mass may be of interest when considering axion searches such as ADMX. Note that the analytical prediction (dashed), observed DM (dotted), and ${\xi }_a$ (blue) curves all coincide, displaying the success of the IPQ model in adapting this particular axion to a viable cosmological outcome.

Figure 4

A realization of the IPQ model with $m_a=6\times {10}^{-10}\mathrm{eV}$, $m_{\chi }=6\times {10}^{-15}\mathrm{eV}$, $F=0.5$, and $Y_i={\chi }_i/S=5$. The top panel shows the evolution of the axion ($\theta$) and $\chi$ field compared to the evolution of the standard QCD axion (${\theta }_{\mathrm{std}}$). The lower panel shows the abundance parameter $\xi \equiv \rho /n_{\gamma }$ for the axion (${\xi }_a$), the $\chi$ field (${\xi }_{\chi }$), their sum, and the standard axion (${\xi }_{a,\mathrm{std}}$). The dashed line indicates the analytical prediction ${\xi }_{a,\mathrm{an}}$ from Eq. (35), and the dotted line shows ${\xi }_{\mathrm{DM},\mathrm{obs}}\approx 2.9\mathrm{eV}$, the observed DM abundance. In this instance, the IPQ model can suppress the abundance of a lighter axion with $f_a$ motivated by the GUT scale, though not down to the observed DM abundance.

Figure 5

The ratio of various abundances in the DPQ model ($\alpha (\chi )=(1+{\chi }^2/S^2)$) to the abundance of axions in the standard theory, $\xi /{\xi }_{a,\mathrm{std}}$, is plotted for various initial field values $Y_i={\chi }_i/S$, showing the enhancement in axion and $\chi$ abundance resulting from tuning this parameter. The ratio ${\xi }_{\chi }/{\xi }_a$ in the DPQ model is also shown. The axion mass is fixed at $m_a={10}^{-10}\mathrm{eV}$, the $\chi$ mass is $m_{\chi }=5\times {10}^{-4}{m}_a$, and the coupling parameter is $F=0.1$. The dashed lines show the analytical estimates, while the points correspond to individual numerical solutions to the field equations.

Figure 6

The ratios of abundances in the IPQ model ($\alpha (\chi )=(1+{\chi }^2/S^2{)}^{-1}$) are plotted for various initial field values $Y_i={\chi }_i/S$, showing the suppression of axion abundance resulting from tuning this parameter. In the upper panel, the sum ${\xi }_a+{\xi }_{\chi }$ is not shown since it is nearly identical to ${\xi }_{\chi }$ as in this case the $\chi$ field is dominant. The axion mass is fixed at $m_a={10}^{-10}\mathrm{eV}$, the $\chi$ mass is $m_{\chi }=0.01m_a$, and the coupling parameter is $F=0.1$. The dashed lines show the analytical estimates, while the points correspond to individual numerical solutions to the field equations.

Figure 7

The ratio of $\chi$ and axion abundances in the DPQ model, ${\xi }_{\chi }/{\xi }_a$, is plotted against the mass of the $\chi$ field, showing that ${\xi }_{\chi }\propto \sqrt{m_{\chi }}$. The axion mass is fixed at $m_a={10}^{-10}\mathrm{eV}$, the initial field value is $Y_i={\chi }_i/S=5$, and the coupling parameter is $F=0.1$. The dashed line shows the analytical estimates, while the points correspond to individual numerical solutions to the field equations.

Figure 8

The ratio of $\chi$ and axion abundances in the IPQ model, ${\xi }_{\chi }/{\xi }_a$, is plotted against mass of the $\chi$ field, showing that ${\xi }_{\chi }\propto \sqrt{m_{\chi }}$. The axion mass is fixed at $m_a={10}^{-10}\mathrm{eV}$, the initial field value is $Y_i={\chi }_i/S=5$, and the coupling parameter is $F=0.1$. The dashed line shows the analytical estimates, while the points correspond to individual numerical solutions to the field equations.

Figure 9

The ratio of $\chi$ and axion abundances in the DPQ model, ${\xi }_{\chi }/{\xi }_a$, is plotted against the coupling parameter $F$, showing roughly that ${\xi }_{\chi }\propto F^{-2}$. The axion mass is fixed at $m_a={10}^{-10}\mathrm{eV}$, the $\chi$ mass is $m_{\chi }=5\times {10}^{-4}{m}_a$, and the initial field value is $Y_i={\chi }_i/S=5$. The dashed line shows the analytical estimates, while the points correspond to individual numerical solutions to the field equations.

Figure 10

The ratio of $\chi$ and axion abundances in the IPQ model, ${\xi }_{\chi }/{\xi }_a$, is plotted against the coupling parameter $F$, showing roughly that ${\xi }_{\chi }\propto F^{-2}$. The axion mass is fixed at $m_a={10}^{-10}\mathrm{eV}$, the $\chi$ mass is $m_{\chi }=0.01m_a$, and the initial field value is $Y_i={\chi }_i/S=5$. The dashed line shows the analytical estimates, while the points correspond to individual numerical solutions to the field equations.