Kinetic Fragmentation of the QCD Axion on the Lattice

TL;DR

This paper investigates kinetic fragmentation of the QCD axion under kinetic misalignment and asks how non-perturbative, inhomogeneous dynamics alter fragmentation and the resulting dark matter abundance. It implements two numerical approaches—the homogeneous backreaction approximation and fully non-perturbative classical lattice simulations using CosmoLattice—to compare against linear theory. The main finding is that non-perturbative lattice dynamics broaden and damp the spectrum, transfer energy to mildly relativistic modes, and typically reduce the final axion DM abundance by a factor of order $O(1)$ relative to the linear approximation, with even larger deviations from the zero-mode-only prediction. This has implications for axion mini-halo formation and motivates a dilution-factor compensation algorithm to reconcile fragmentation with the observed DM abundance.

Abstract

Kinetic misalignment, one of the most compelling scenarios for the non-thermal generation of axion dark matter, is generally accompanied by axion fragmentation, a process in which the energy of the axion condensate is transferred to its perturbations. The dynamics of fragmentation, at least in the context of dark matter production, have so far been studied semi-analytically using perturbation theory. In this work, we present the first classical lattice simulation of kinetic axion fragmentation in the context of dark matter production, focusing on parameters relevant to the QCD axion. Our findings indicate that the non-perturbative dynamics captured by the lattice lead to a significantly broader spectrum of axion fluctuations, with a sustained transfer of energy to mildly relativistic modes and with smaller occupation numbers compared to the linear approximation. As a consequence, the final dark matter abundance is typically O(1) lower than in the linear approximation, which is itself O(1) lower than the zero-mode-only prediction. This broadening and suppression of the spectrum could have a significant impact on axion mini-halo formation, one of the main experimental handles on kinetic fragmentation.

Figures (9)

• Figure 1: The landscape of the relevant parameter space for axion dark matter. The part of the QCD axion highlighted in blue is the parameter space studied in this work. The dark shaded region is the parameter space already excluded by haloscope experiments while the light gray area corresponds to the parameter space accessible by future haloscope experiments. The data in this plot has been adapted by AxionLimits.
• Figure 2: Left panel: evolution of the kinetic and potential energy densities of the zero mode. Right panel: evolution of the kinetic and potential energy of the zero mode along with the energy of perturbations in red. In this case the backreaction is treated according to the homogeneous approximation outlined in Sec. \ref{['Sec:homogeneous-backreaction']}.
• Figure 3: The evolution of the rescaled energy densities in the lattice analysis is displayed in solid lines for various values of $n$. Dashed lines show the evolution of the energy density of fluctuations in the homogeneous backreaction approximation.
• Figure 4: Evolution of the Power Spectrum fo the scalar field for $n=500$, from the beginning of the simulations, $a=1.0$ to $a=2.5$, with steps of $\Delta a = 0.1$. Solid lines correspond to lattice simulations and dashed lines to homogeneous backreaction.
• Figure 5: Upper panel: Power spectrum of the scalar field at the moment of fragmentation, defined according Eq. (\ref{['eq:powerspectrum']}), for all $n$'s. Solid lines correspond to lattice simulations and dashed lines to homogeneous backreaction. Note that $n=50$ is not included, as it does not completely fragment. Lower panel: Equivalent to the left panel for $a=2.5$, i.e. at the end of the evolution.