Hey @lemouth long time no see ^^
I'm curious, are those freezing scenarios based on the hypothesis of Dark Matter being weakly interacting massive particles (WIMPs) and our knowledge of weak interaction or is this a more specific property?
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Indeed. it was a long time :)
We are talking about feeble interactions that are many orders of magnitude weaker than the weak interactions. WIMPs are in fact thermal relics (they were in equilibrium with the thernal bath in the early universe) whilst FIMPS (feebly interacting massive particles) are never reaching this thermal equilibrium. They are totally decoupled.
In short, a WIMP will freeze-out no matter what.