Resolving the QCD Axion Domain Wall Problem with a Light Axion

Abstract

We propose two novel solutions to the domain wall problem of the QCD axion by introducing a massless or light axion that also couples to gluons. The first solution applies when the new axion forms strings after inflation. Due to its mixing with the QCD axion, domain walls of the QCD axion are bounded by these strings and confined into cosmologically safe string bundles. This scenario predicts the existence of such string bundles, which may survive until today and leave observable signatures, such as gravitational waves, cosmic birefringence, and CMB anisotropies. The simultaneous detection of the QCD axion and any of these cosmological signatures would serve as a smoking-gun signal. The second solution assumes a homogeneous initial condition for the new axion. If it is sufficiently light, its potential temporarily induces a bias in the QCD axion potential before the onset of oscillations, rendering the domain walls unstable. In both scenarios, the Peccei-Quinn mechanism remains effective, and the strong CP problem is not reintroduced. We identify the viable parameter regions and discuss the resulting dark matter abundance.

Figures (7)

• Figure 1: Schematic illustration of string bundle formation. The circles with $a$ and $\phi$ represent cosmic strings of $a$ and $\phi$, respectively, and the circles with $\bar{a}$ and $\bar{\phi}$ represent their corresponding anti-strings. The black lines connecting strings represent domain walls. Left panel: When the domain wall tension is too small to pull the strings together, the string-wall network stretches over cosmological scales. Right panel: Once the domain walls pull the strings together, the strings and their anti-strings annihilate with each other, and a specific combination of strings forms a string bundle.
• Figure 2: $T_\mathrm{DW}$ as a function of $F$. The horizontal dashed line denotes $T_\mathrm{DW} = T_\mathrm{QCD}$. The behavior of $T_\mathrm{DW}$ changes on either side of the dashed line.
• Figure 3: The temperature when the string bundles form, $T_\mathrm{bf}$, as a function of $F$. The colored lines represent different values of the tension of $\phi$ strings, $\mu_\phi$. The horizontal dashed line denotes $T_\mathrm{bf} = T_\mathrm{QCD}$. Here, we evaluate $T_\mathrm{bf}$ by taking the smaller value of $T_\mathrm{DW}$ in Eq. \ref{['eq: TDW']} and $T_\mathrm{bf}$ in Eq. \ref{['eq: Tbf']}.
• Figure 4: The QCD axion abundance from the string-wall network as a function of the decay constant $f_\phi$, for the QCD axion decay constant $F = 10^{12},\,10^{11},\,10^{10}\,10^9$ GeV from top to bottom. The gray shaded region indicates where the abundance exceeds the observed dark matter abundance $\Omega_c h^2 \simeq 0.12$.
• Figure 5: Constraints in the $(f_\phi,T_{\rm dec})$ plane with $c=0.5$ and $\phi_{\rm ini}=f_\phi$. The blue-shaded region indicates overproduction of the light ALP, while the orange-shaded region shows where $A_L$ settles to its potential minimum before the domain-wall decay. The solid and dashed lines correspond to $f_a = 2\times10^8\,{\rm GeV}$ and $2\times10^9\,{\rm GeV}$, respectively.