Dependence of freeze-out spectra on Γ/H during radiation-dominated expansion

Investigate the dependence of thermalization and the resulting freeze-out momentum spectrum on the ratio Γ/H, where Γ ≡ n⟨σv⟩ is the interaction rate and H is the Hubble rate, in a radiation-dominated cosmological expansion; determine how different Γ/H regimes shape the momentum-resolved distribution governed by the Boltzmann equation and identify the conditions under which freeze-out occurs.

Background

In cosmological settings, thermalization proceeds only if the interaction rate Γ ≡ n⟨σv⟩ exceeds the Hubble expansion rate H; otherwise, expansion redshifts momenta more rapidly than collisions can redistribute them, leading to freeze-out.

The authors note that their framework supports radiation-dominated expansion and can explicitly track the competition between Γ and H, but they explicitly defer a systematic study of how Γ/H controls the freeze-out spectrum, identifying this as future work.

References

In a cosmological setting, thermalization requires the interaction rate Γ ∼ n ⟨σ v⟩ to exceed the Hubble rate H ∼ 1/(2t) in radiation domination. When Γ < H, the expansion redshifts momenta faster than collisions can redistribute them, and the distribution freezes out. The code supports radiation-dominated expansion and can track this competition explicitly; a study of the Γ/H dependence and the resulting freeze-out spectrum is left for future work.

— Boltzmann Equation Solver for Thermalization  (2603.28848 - Yoon, 30 Mar 2026) in Section 6 (Discussion)

Indeed, even whether DM was once in thermal equilibrium with the bath before decoupling from it (the freeze-out mechanism ), or whether it was produced gradually from the thermal bath during the evolution of the Universe (the freeze-in mechanism ), is still entirely unknown.

— A relook at a low reheating temperature: Freeze-in versus Freeze-out  (2609.26348 - Choudhury et al., 22 Sep 2026) in Section 1, Introduction