Nonperturbative overproduction of axionlike particles via derivative interactions

Axionlike particles (ALPs) are quite generic in many scenarios for physics beyond the Standard Model. They are pseudoscalar Nambu-Goldstone bosons that appear once any global $U(1)$ symmetry is broken spontaneously. The ALPs can gain mass from various nonperturbative quantum effects, such as anomalies or instantons. ALPs can couple to the matter sector including a scalar condensate such as inflaton or moduli field via derivative interactions, which are suppressed by the axion decay constant, $f_{\chi }$. Although weakly interacting, the ALPs can be produced abundantly from the coherent oscillations of a homogeneous condensate. In this paper we will study such a scenario where the ALPs can be produced abundantly, and in some cases can even overclose the Universe via odd- and even-dimensional operators, as long as $f_{\chi }/{\mathrm{\Phi }}_{\mathrm{I}}\ll 1$, where ${\mathrm{\Phi }}_{\mathrm{I}}$ denotes the initial amplitude of the coherent oscillations of the scalar condensate, $\varphi$. We will briefly mention how such dangerous overproduction would affect dark matter and dark radiation abundances in the Universe.

Figure 1

The above figure shows the time evolution of $\alpha (z)/m_{\varphi }$ (solid curve) and ${\omega }_k^2(z)/m_{\varphi }^2$ (dashed curve) for $f_{\chi }=M_P/25$. The evolution of $\alpha (z)/m_{\varphi }$ becomes negative roughly half the time period of oscillations, and becomes singular at the times defined by Eqs. (23) and (24), this results in tachyonic instabilities. For $k<m_{\chi }$, the evolution of ${\omega }_k^2(z)/m_{\varphi }^2$ becomes negative for less than half the time period of oscillations as long as $\mathrm{\Phi }/f_{\chi }>1$ (see the upper panel), whereas for $k>m_{\chi }$, the evolution ${\omega }_k^2(z)/m_{\varphi }^2$ becomes negative only in the vicinity of singular points (see the lower panel). Here time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 2

The evolution of ${\rho }_{\chi }/({\rho }_{\varphi ,I}{a}^{-3})$ during part of the first oscillation of the $\varphi$ field.

Figure 3

The above figures show the time evolution of $\alpha /m_{\varphi }$ (solid curve), and ${\omega }_k/m_{\varphi }$ for $k\gg m_{\chi }$ (dot-dashed curve) and $k\ll m_{\chi }$ (dashed curve) for $f_{\chi }\simeq 1.1M_P$. For $m_{\chi }\ll k$, ${\omega }_k$ does not oscillate and redshifts with the expansion of the Universe, whereas for $k\ll m_{\chi }$, ${\omega }_k$ oscillates with double the frequency of $\varphi$ field, and moves toward its maximum value, $m_{\chi }$, as the amplitude of the oscillations dies out with cosmic expansion. Here time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 4

Same as Fig. 3, but for $f_{\chi }=M_P/25$. Note that the damping coefficient, $\alpha$, now oscillates to negative values twice per each oscillation of the $\varphi$ field.

Figure 5

The time evolution of ${\tilde{\omega }}_k^2/m_{\varphi }^2$ for $k=3m_{\varphi }$ and $m_{\chi }\ll k$, where the effect of expansion is ignored. The ${\tilde{\omega }}_k^2$ becomes negative for two short periods of time during each oscillation of $\varphi$. Here time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 6

The above figure shows time evolution of ${\rho }_k$ for $k=3m_{\varphi }$ and $m_{\chi }\ll k$, where the effect of expansion is neglected. Here time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 7

Same as Fig. 5 but for $m_{\chi }=3m_{\varphi }$ and $k\ll m_{\varphi }$, without taking into account expansion.

Figure 8

The evolution of $|{\dot{\tilde{\omega }}}_k/{\tilde{\omega }}_k^2|$ in time for $m_{\chi }=3m_{\varphi }$ and $k\ll m_{\varphi }$, where the effect of expansion is ignored. One can see easily that the adiabaticity gets violated around the intervals where ${\tilde{\omega }}_k^2$ becomes tachyonic. This takes place twice per each oscillation of $\varphi$. Here the time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 9

Same as Fig. 6, but for $m_{\chi }=3m_{\varphi }$ and $k\ll m_{\varphi }$, without taking into account expansion.

Figure 10

The evolution of ${\rho }_k$ in time for $f_{\chi }=M_P/25$ and $m_{\chi }<k\ll m_{\varphi }$ where the effect of expansion is included. Here the time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 11

Same as Fig. 5, but now the cosmic expansion is included. One can see that the tachyonic instabilities become dominant within few oscillations of $\varphi$ field. The corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 12

The above figure shows the evolution of ${\rho }_k$ in time, where the cosmic expansion is included. Here time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 13

The above figure shows the evolution of ${\rho }_{\chi }/{\rho }_{\varphi ,I}$ in time for $m_{\chi }\ll m_{\varphi }$, where $m_{\varphi }=10^{13}\mathrm{GeV}$. Here time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis. This analysis includes cosmic expansion.

Figure 14

Same as Fig. 7, but now cosmic expansion effect is included. One can see that the tachyonic instabilities become important within few oscillations of $\varphi$. The corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 15

Same as Fig. 8, but now the cosmic expansion is taken into account. The evolution of ${\tilde{\omega }}_k$ seizes to be nonadiabatic after a few oscillations of $\varphi$. The corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis.

Figure 16

The above figure shows the time evolution of ${\rho }_k$. As expected, the excitation of such heavy ALPs takes place during the first few oscillations of $\varphi$. Here time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis. This analysis includes cosmic expansion.

Figure 17

The above figure shows the time evolution of ${\rho }_{\chi }/{\rho }_{\varphi ,I}$ for $m_{\chi }=3m_{\varphi }$, where $m_{\varphi }=10^{13}\mathrm{GeV}$. Here time is measured in units $m_{\varphi }^{-1}$; the corresponding number of $\varphi$ oscillations is shown on the upper horizontal axis. This analysis includes cosmic expansion.

Figure 18

The above figure shows ${\rho }_{\chi }/{\rho }_{\varphi ,I}$ as a function of ratio $f_{\chi }/{\mathrm{\Phi }}_{\mathrm{I}}$ after five $\varphi$ oscillations for $m_{\varphi }=10^{10}\mathrm{GeV}$ (thin curves) and $m_{\varphi }=10^{13}\mathrm{GeV}$ (thick curves). The solid (dashed) curves corresponds to light (heavy) ALPs, respectively. This analysis includes cosmic expansion.