First-order phase transitions change the game for axion dark matter
A first-order phase transition can generate the axion mass, making it non-zero only inside expanding true-vacuum bubbles, qualitatively altering misalignment production. Lattice simulations in an expanding universe reveal two regimes. For rapid transitions, oscillations are delayed until bubble percolation, enhancing the relic abundance. For slower transitions, expanding bubbles create spatial gradients that suppress the effective misalignment angle through the bubble misalignment mechanism. A semi-analytical expression for the relic density is derived, providing a unified description of both regimes and accurately reproducing simulation results. This mechanism also modifies isocurvature perturbations and the small-scale matter power spectrum, with significant implications for axion minicluster formation.
Context
The dark matter problem is one of the main mysteries of modern physics. Already Vera Rubin showed that galaxies rotate as if they contain much more mass than can be seen. One of the best candidates is the axion — an ultra-light particle proposed to solve the strong CP problem in the Standard Model. It is usually assumed that axions are produced in the early universe via the misalignment mechanism: the field freezes away from the minimum of the potential, then begins to oscillate, producing cold dark matter. However, what if the axion mass turns on not smoothly, but abruptly — as a result of a cosmological first-order phase transition? It is this scenario, inspired by the ideas of Stephen Hawking about quantum fluctuations in the early universe and the possible violation of entropy conservation in such processes, that the authors considered.
Methods
The modeling used a lattice in an expanding universe governed by the Friedmann–Lemaître equations derived by Georges Lemaître. Initially the axion field is homogeneous and frozen, but then true vacuum bubbles begin to nucleate, inside which the axion mass abruptly assumes a finite value. The nucleation rate is given by a phenomenological law, and the bubbles expand with a constant wall velocity. The equation of motion was solved using the leapfrog method, taking into account the nonlinearity of the potential and cosmological expansion. To avoid spurious oscillations at the bubble boundaries, finite differences were used instead of spectral methods. The key parameter is the ratio of the phase transition duration to the axion oscillation period.
Results
Simulation results showed two limiting regimes. In fast transitions, when bubbles collide before the field can start oscillating, the mass turn-on simply delays the onset of oscillations until percolation. This boosts the relic density: the axion "forgets" to get diluted by expansion. The numerical boost factor ξ can reach hundreds. In slow transitions, conversely, shock waves form in front of the bubble walls, reducing the oscillation amplitude inside. This mechanism, dubbed bubble misalignment, was first proposed in 2024 and is now confirmed in a realistic cosmology. The resulting semi-analytical formula describes both regimes with ~10% accuracy and predicts that to explain all of dark matter, the axion decay constant must be lower than usual.
Implications
The finding means that standard predictions for axion cosmology may be significantly corrected if phase transitions occurred in the early universe. This forces a revision of estimates for the axion mass and coupling constant, as well as the interpretation of observational data. In particular, the shift in the start time of oscillations alters the isocurvature spectrum and affects the formation of mini-clusters — clumps of dark matter that might be detectable with the JWST telescope.
Future development
In the future, researchers plan to apply these ideas to the QCD axion, whose mass depends on temperature even before the phase transition. This will complicate the picture but may lead to a richer phenomenology. Moreover, studying the stochastic gravitational-wave background from the same phase transition will provide an independent way to test the model. Work is already underway to embed the scenario into a full theory with Peccei–Quinn gauge symmetry.
Impact
The results will impact areas: early universe cosmology, particle physics beyond the Standard Model, astrophysics of black holes (via superradiance constraints), and observational cosmology using JWST and Lyman-α forest data.
Next steps
Next steps include detailed modeling of axion strings in the presence of a phase transition and calculating the gravitational wave signal in specific ultraviolet completions. Public adaptation of the code is also planned.
Key open problems
The work is directly connected to the unsolved problems of the nature of dark matter and the strong CP problem. The bubble misalignment mechanism also sheds light on a general question: how do non-equilibrium processes in the early universe shape the relic abundance of particles?
🎯 If the phase transition had occurred a little later, the axions could have supercooled, and we would be living in a very different universe — with much denser mini-clusters that might have already collapsed into black holes.
Key numbers
- Ω_DM h^2: 0.12
- minimum transition temperature T_p: 0.3 MeV
- typical value of H_⋆/M_ϕ in simulations: 0.05
- maximum boost factor ξ: ~10^3
- number of sampling points: 10^5