This paper studies a way to avoid a long‑standing cosmological upper limit on the axion decay constant, often written f_a ≲ 10^12 GeV. The authors show that if quantum chromodynamics (QCD, the theory of the strong force) becomes very strong during cosmic inflation, the axion field can relax early. That early relaxation reduces the axion’s energy density today and removes the usual cosmological bound on f_a.

The researchers implement this idea inside a simple grand unified theory based on SU(5). They consider two ways to make QCD strong during inflation. One is a direct coupling between the inflaton (the field that drives inflation) and the gauge fields. The other is a kind of symmetry restoration: during inflation the SU(5) symmetry can be restored and, because the SU(5) gauge coupling runs with energy, this can drive QCD into a strong, confining regime. In their setup the inflaton field S controls both the size of the Peccei–Quinn (PQ) order parameter and an effective gauge coupling α_eff(S/M) that appears multiplying tr G_{μν}G^{μν}.

The basic physical effect is simple. If QCD is strong early, the axion gets a mass while the universe still inflates. If that early axion mass is larger than the Hubble expansion rate during inflation, the axion undergoes damped oscillations and settles near the minimum of its potential. This reduces the initial misalignment angle—the main source of axion dark matter in the standard picture—and so lowers the axion energy density seen today. The authors argue this works across the usual axion constructions: PQ models with extra scalars (DFSZ), models with heavy fermions (KSVZ), and even the so‑called gauge (two‑form) axion formulation.

An important conceptual point emphasized here is that the axion degree of freedom can exist even if the usual PQ scalar has vanishing vacuum value during inflation. In that case the symmetry is broken instead by a fermion condensate, the ’t Hooft determinant, and the axion appears as the phase of that condensate. In the DFSZ case this early condensate is related to ordinary quark condensation and resembles an early‑universe version of the η′ meson. In all studied cases the early confinement gives the axion a potential and allows its energy to be diluted enough that arbitrarily large f_a can be compatible with axion dark matter.