This paper studies a class of dark matter that is made when a heavier particle in a hidden “dark sector” decays late in the early universe. The decay produces a light dark matter particle that is not in thermal equilibrium with ordinary matter. Because these particles can be born with relatively large speeds, they can wash out small clumps of matter. The authors use observations of the Lyman‑α forest — patterns of hydrogen absorption in quasar light that probe small-scale matter structure — to test and constrain this scenario.

The particle physics model they analyze contains a heavy scalar mediator called ϕ, a dark matter particle χ, and a right-handed neutrino N. The heavy ϕ sits in the thermal bath early on, freezes out, and then decays at late times via ϕ → χ + N. The χ particles produced this way have a non‑thermal momentum distribution. To follow that distribution in an expanding universe the authors solve Boltzmann equations that include cosmic redshift. The model has five free parameters: the masses mϕ, mχ, mN, the decay coupling yDS, and the thermal coupling λHϕ that sets the parent abundance.

From their solutions the authors compute the dark matter phase‑space or momentum distribution and the linear matter power spectrum (the amplitude of density variations on different scales in the early universe). Because observational bounds on small scales are often quoted for thermal “warm dark matter” (WDM) models, they map the non‑thermal χ distribution to an equivalent thermal WDM model. This allows them to apply recent Lyman‑α forest limits on how much small‑scale power may be suppressed. They also combine these limits with constraints from Big Bang nucleosynthesis (BBN), which restricts changes to the early thermal history.

The main outcome is that, under the assumptions of their analysis, sub‑GeV dark matter is tightly constrained. In particular, masses lighter than about 10−1 GeV are excluded for the scenario in which χ makes up all of the dark matter. The authors note that the freeze‑in production channel (a separate, earlier production process) can be neglected when the decay coupling is small, yDS ≲ 2×10−12, so the late decay component dominates the momentum distribution that matters for structure suppression. They also use a zero‑momentum approximation for the heavy parent ϕ before decay; they report that this is accurate because ϕ’s momentum gets heavily redshifted before it decays.