Axion Cosmology with Multi-Branch Yang-Mills

TL;DR

This work reveals that the multi-branch vacuum structure of Yang-Mills theories, encoded in a θ-dependent energy landscape, profoundly impacts axion cosmology when the axion mass arises from a YM sector. By linking the axion potential to the tunneling rate between adjacent branches, the authors show that inflation can selectively populate excited YM vacua even in cold, unreheated sectors, and that the post-inflationary axion dynamics can trigger strongly first-order phase transitions with ultra-relativistic bubble walls. These transitions can generate stochastic gravitational waves, primordial black holes, or hidden-sector particle production, constituting new predictions of the Axiverse; standard axion cosmology is recovered only if these multi-branch dynamics are suppressed. The study also develops a hilltop axion mechanism whereby sufficient decay constants $f_\phi \gtrsim M_{\rm pl}$ place the observable patch near the hilltop, enabling cascade tunneling and observable cosmological signatures that are absent in conventional scenarios.

Abstract

It is known that Yang-Mills theories, especially in the large-$N$ limit, exhibit a $θ$-vacuum structure with a multi-branched vacuum energy. In this work, we demonstrate that this multi-branch structure can play a crucial role in axion cosmology when the axion acquires its mass from the Yang-Mills sector, even when that sector is never reheated by the inflaton. The key observation is that the axion potential is directly tied to the tunneling rate between adjacent branches. We find qualitatively new phenomena, including a new class of first-order phase transitions, bouncing bubbles, and nested "bubbles-within-bubbles." When the axion has a decay constant around the Planck scale, as motivated by the string Axiverse, the axion can be driven near the hilltop by inflationary dynamics, allowing the phase transition to be triggered. The associated energy release can be large enough to generate a significant stochastic gravitational-wave background, produce primordial black holes, or populate the Yang-Mills sector with particles. These phenomena represent novel predictions of the Axiverse and should be taken into account when assessing the cosmological impact of axions or axion-like particles. To recover conventional axion cosmology, one must suppress or avoid the dynamics discussed in this work.

Figures (5)

• Figure 1: Schematic picture of the vacuum energy $E(\theta)$. Each smooth curve (composed of solid and dashed segments) corresponds to a vacuum labeled by an integer $k$. The solid curve represents the true vacuum, while the dashed curves represent metastable vacua. The $2\pi$ periodicity of $\theta$ is realized through the presence of multiple branches.
• Figure 2: Schematic picture of the tunneling near the hilltop. Blue, red, and green lines show the different vacuum branches. The tunneling occur between neighboring branches.
• Figure 3: A simple 2D simulation of the "bubbles-within-bubbles" scenario, assuming an additional cascade of tunneling events. The blue (red) circles denote the primary (secondary) bubbles.
• Figure 4: Time evolution of $S_4$, which governs the bubble nucleation rate in Eq. (\ref{['rate1']}). The blue dashed (red solid) curve shows the result with $|\bar{\theta}_i|\lesssim 1$ ($\bar{\theta}_i\sim \bar{\theta}_\text{max}$) with $\bar{\theta}_i^{-3} \bar{S}=10$$(\delta\bar{\theta}_i^{-3} \bar{S}=10)$. A radiation-dominated Universe is assumed.
• Figure 5: The simulation of the axion field configuration at different $t$ with the wall background. The left panel denotes the result with smaller $t=(0-20) /m_\phi$ while the right panel denotes the configuration at the $t=(20-50) /m_\phi$. The wall sweeps the whole area from $t=0-50/m_\phi$.