Axion misalignment as a synchronization phenomenon

TL;DR

This work reframes the axion misalignment mechanism as a dynamical synchronization phenomenon, treating the axion field as a locally coupled, damped phase network with a time-dependent coupling set by cosmic expansion. By introducing a complex order parameter $R(t)e^{i\Psi(t)}$ and a collective phase $\Psi(t)$, the authors show that macroscopic phase coherence can emerge dynamically from incoherent initial configurations, making the misalignment angle an emergent variable only after phase ordering. The analysis preserves the standard relic abundance calculation when coherence is established (with $\rho_a(t)\simeq \frac{f_a^2}{2}[\dot{\Psi}^2+m_a^2(T)\Psi^2]$) and clarifies the role of the oscillation condition $3H(T_{\rm osc})\simeq m_a(T_{\rm osc})$ as the point where a well-defined collective angle is justified. The framework reinterprets anthropic small-angle arguments as reflections of phase-ordering efficiency and links to the broader idea that fine-tuning in cosmology may arise from emergent collective dynamics, with potential extensions to higher dimensions and defect dynamics in axion cosmology.

Abstract

We propose a dynamical reinterpretation of axion misalignment as an emergent collective phenomenon. Drawing an explicit parallel between axion field dynamics and synchronization in coupled oscillator systems, we show that a macroscopic axion phase can arise dynamically from initially incoherent configurations through gradient-driven ordering in an expanding Universe. In this framework, the misalignment angle is not a fundamental initial condition but a collective variable that becomes well defined only once phase coherence develops. Using a simple lattice model, we illustrate how the collective phase is selected prior to the onset of axion oscillations, providing a dynamical basis for the standard misalignment picture. This perspective offers a new way of organizing axion initial-condition sensitivity, reframes anthropic small-angle arguments in terms of phase-ordering efficiency, and suggests a broader connection between fine-tuning and emergent collective dynamics in the early Universe.

Figures (4)

• Figure 1: Evolution of the order parameter $R(T)$ as a function of temperature. Starting from random initial phases, the system develops macroscopic coherence ($R=\mathcal{O}(1)$) well before the onset of axion oscillations.
• Figure 2: Emergent collective phase $\Psi(T)$. At high temperature, where $R\simeq0$, the phase fluctuates strongly and has no physical meaning. Once coherence is established, $\Psi(T)$ stabilizes and becomes a well-defined macroscopic axion angle.
• Figure 3: Comparison between the axion mass $m_a(T)$ and the Hubble scale $3H(T)$. The intersection defines the conventional oscillation temperature $T_{\rm osc}$. At this temperature, the system is already in a coherent phase, justifying the identification of the misalignment angle with the emergent collective phase $\Psi(T_{\rm osc})$.
• Figure 4: Snapshots of the axion phase field $\theta_i$ at representative temperatures (top to bottom: decreasing $T$). The field evolves from a highly disordered configuration at high temperature to a smooth but nonuniform profile at late times. Residual spatial structure reflects conserved topological winding in one dimension.