Acoustic Misalignment Mechanism for Axion Dark Matter

TL;DR

Acoustic misalignment mechanism (AMM) identifies sound-wave fluctuations in a rotating PQ field as a novel axion dark matter production channel, supplementing kinetic misalignment. The authors develop a formalism to track zero-mode rotation and linear perturbations through pre-kination and kination, computing the resulting axion abundance and comparing it to KMM. They show AMM can dominate DM production when the radial-direction mass is large, and that AMM-generated axions can be warm enough to impact structure formation, with broad implications for axion searches and axiogenesis scenarios. The work opens new parameter-space regions and connects dark matter production to baryogenesis in axion-rotation cosmologies.

Abstract

A rotation in the field space of a complex scalar field corresponds to a Bose-Einstein condensation of $U(1)$ charges. We point out that fluctuations in this rotating condensate exhibit sound-wave modes, which can be excited by cosmic perturbations and identified with axion fluctuations once the $U(1)$ charge condensate has been sufficiently diluted by cosmic expansion. We consider the possibility that these axion fluctuations constitute dark matter and develop a formalism to compute its abundance. We carefully account for the growth of fluctuations during the epoch where the complex scalar field rotates on the body of the potential and possible nonlinear evolution when the fluctuations become non-relativistic. We find that the resultant dark matter abundance can exceed the conventional and kinetic misalignment contributions if the radial direction of the complex scalar field is sufficiently heavy. The axion dark matter may also be warm enough to leave imprints on structure formation. We discuss the implications of this novel dark matter production mechanism -- {\it acoustic misalignment mechanism} -- for the axion rotation cosmology, including kination domination and baryogenesis from axion rotation, as well as for axion searches.

Figures (17)

• Figure 1: Sound waves of the PQ charge density $n_\theta$ are produced by cosmic perturbations. After the dilution of the charge density by cosmic expansion, sound waves become axions. The dotted line shows the average charge density.
• Figure 2: The acoustic misalignment mechanism (AMM) and the kinetic misalignment mechanism (KMM) can explain the observed dark matter abundance in the orange-shaded region, with the labels showing which mechanism can dominate. In the green-shaded region and on the sold green line, the observed baryon asymmetry can also be explained by axiogenesis via the weak sphaleron process. Further details are provided in Secs \ref{['sec:implications']} and \ref{['sec:axiogenesis']}.
• Figure 3: A schematic showing post-inflationary cosmology in nearly quadratic models. The energy density in the rotating axion (orange line) scales as matter initially and transitions to kination when the radius of rotation reaches the potential minimum. This may lead to a period of axion domination in the early universe. The sound-wave mode of the fluctuations (yellow line) around the rotating zero mode is produced from cosmic perturbations and evolves. The sound waves become axion fluctuations at the bottom of the potential. The energy density of the axion fluctuations initially dilutes like radiation, and becomes non-relativistic as the mass of the axion becomes important. The axion fluctuations then transition to matter-like behavior and can make up the entirety of dark matter today. There can be nonlinear evolution of the axion fluctuations around this transition as discussed in Sec. \ref{['sec:NL']}.
• Figure 4: The equations of states for the two-field model with various $r_P$ values as labeled, for the log potential, and for the quartic potential. The scale factor $R_{1/2}$ is defined when the equation of state is $w=1/2$.
• Figure 5: The dispersion relations of the two perturbation modes around the rotating background for the log-potential model. The solid lines correspond to $r= 10^{3}N_{\rm DW}f_a$ (nonzero $U(1)$ charges), while the dashed lines are for $r= N_{\rm DW}f_a$ (no $U(1)$ charges). In both cases, there is a gapless mode corresponding to phonons shown in blue, and the massive radial excitation mode is shown in red.