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Low temperature reheating

Physics Asked on July 14, 2021

I have a question about the Low reheating temperature. [https://arxiv.org/pdf/1406.0012.pdf]

I’m confused about the order of the events and maybe in their definitions. Everything is summarized in this graph.
enter image description here
I have in mind:
At the end of inflation, the inflaton field decaying to radiation.
Expansion is faster during reheating (start at the end of inflation) than radiation epoch since entropy is produced during (a part of ?) reheating (actually during inflaton’s decay).
Now I want to introduce the dark matter freeze-out.

I don’t understand why ‘Due to a faster expansion of the Universe, for low T$_R$ the freeze-out occurs slightly earlier…’ What is the link between the freeze-out temperature T$_{fo}$ and T$_{R}$?

And ‘ If the decay of the inflaton stopped at T$_{fo}$, the DM abundance would be higher in the low T$_{R}$ scenario. However, a continuous entropy production keeps diluting it until the reheating temperature is reached. ‘ But if the inflaton’s decay is already stopped why the entropy still be produced?

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