Trapped and Unstable: Axion-like particle fragmentation at finite temperature

Abstract

We investigate the emergence of a resonant behavior in axion-trapped misalignment models featuring finite-temperature potential barriers. As the temperature decreases and the field is released from its trapped configuration, inhomogeneities are exponentially amplified through an instability in their equation of motion, leading to the fragmentation of the axion field. We show that this process constitutes a novel source of gravitational waves (GWs), analogous to those generated in zero-temperature axion fragmentation, but with distinct characteristics. We quantify the resulting GW spectrum, identifying the peak frequency and amplitude associated with the inhomogeneous axion dynamics. Our results indicate that the GW signal can be enhanced by up to two orders of magnitude compared to the standard fragmentation scenario, while exhibiting a markedly different spectral shape. The parameter space featuring both strong GW signals and reproducing the correct dark matter abundance is, however, limited.

Figures (5)

• Figure 1: Exemplary ALP potential \ref{['eq:trapping_potential']}, employing the indicated benchmark parameters. Initially, a thermal barrier prevents the ALP from rolling. As the barrier vanishes around $T_{\hbox{\scriptsize rel}}$, the false minimum becomes a saddle point and oscillations about the true minimum start. The numerical evaluation of the finite-temperature release angle (dashed gray) agrees well with our approximate solution \ref{['eq:theta_rel']}.
• Figure 2: Viable parameter space for ALP fragmentation in the $m_\phi-\Lambda_{\cancel{{\hbox{\tiny\rm{PQ}}}}}$ parameter space. Each panel corresponds to a different choice of the ALP decay constant, $f_\phi \in \{10^{11},10^{13},10^{15},10^{17}\}\,\mathrm{GeV}$. Solid (dashed) lines employ $q=2$ ($q=1$), while the black lines indicate the parameter space where the correct CDM abundance is produced. In the blue-shaded region, the trapping period becomes too extended such that the ALP overcloses the Universe at the onset of oscillations. In the orange-shaded regime, the setup reduced to ordinary misalignment, where fragmentation is inefficient (cf. eq. \ref{['eq:m_over_H_est']}). Generally, smaller $f_\phi$ and larger $q$ open up the viable parameter in terms of $\Lambda_{\cancel{{\hbox{\tiny\rm{PQ}}}}}$. In addition, large decay constants severely limit the mass range where the ALP can be CDM.
• Figure 3: Projected present GW spectra for the benchmark parameters from table \ref{['tab:benchmarks']}. The colored curves indicate the power-law integrated sensitivities of several future GW experiments. The black solid lines correspond to benchmarks that reproduce the correct CDM abundance. That is, ALPs are overproduced above the gray dotted line and the dashed spectra can only be realized through further model building to suppress the relic abundance. By varying the ALP mass and decay constants, the spectral peak moves into the sensitivity regions of future observatories. The red star indicates our analytic estimate of the peak \ref{['eq:Omega_GW_estimate_final']}, which correctly describes the scaling behavior of the GW signal.
• Figure 4: Exemplary simulation of the fragmentation process, employing $m_\phi = 10^{-19}\,\mathrm{eV}$, $f_\phi =$, $\Lambda_{\cancel{{\hbox{\tiny\rm{PQ}}}}} \approx 7.5\times 10^{-9}\,\mathrm{GeV}$, $\delta = 1$, $n=2$, and $q=2$. Top: Energy densities of the zero mode (blue) and the fluctuations (orange), normalized to the total energy density of the Universe, as a function of the scale factor. Bottom: Oscillation amplitude of the zero mode. Around $a \approx 1.36 a_{\hbox{\scriptsize osc}}$, the fluctuation energy density becomes comparable to the one of the zero mode. Then, backreaction sets in and dampens the oscillations.
• Figure 5: Spectral ALP (top) and GW (bottom) energy density at different times during the simulation, using the model parameters from fig. \ref{['fig:benchmark_sim']}. We display the spectra as a function of the physical momenta $k/a_\star$, normalized to the Hubble rate at the time of production. The dashed line in the UV corresponds to our estimate of the fastest growing mode \ref{['eq:peak_momentum']}, which also sets the peak of the GW spectrum.