Scalar dark matter produced by misalignment — the field starts displaced from its potential minimum and oscillates when the Hubble rate drops below the mass — has a problem. During inflation, the field acquires superhorizon quantum fluctuations uncorrelated with ordinary matter fluctuations. These produce isocurvature perturbations: variations in the dark-matter-to-photon ratio from place to place. The cosmic microwave background constrains isocurvature modes tightly. For high-scale inflation, standard misalignment is in tension with observations.
Thermal misalignment changes the production mechanism. Interactions with the thermal bath create a finite-temperature potential that pushes the scalar field to large values during the radiation era, then releases it as the universe cools. The relic abundance depends on particle properties — the coupling strength and mass — rather than on the unknowable initial field value.
The key finding: thermal misalignment also suppresses isocurvature perturbations. The mechanism is a late-time phase offset between the background zero mode and the superhorizon perturbations. The thermal potential drives the background and the perturbations along different trajectories, so that by the time oscillations begin, the perturbations have lost their correlation with the initial inflationary displacement. The density contrast between the dark matter field at different spatial points is reduced — not because the perturbations vanish, but because the phase relationship between them and the background has been scrambled by the thermal dynamics.
The structural point: the same thermal interaction that sets the relic abundance also erases the problematic fluctuations. There is no separate mechanism needed for isocurvature suppression — it is a consequence of the production mechanism itself.
(arXiv:2603.18132)