Do Dark Matter Particles Cool Over Time Due to the Stretching of Space?

DarkMatterHol
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Does Dark Matter have a temperature - obey the laws of thermodynamics?
 
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Well the C in \lambda CDM (a favoured cosmological model) stands for cold, as opposed to hot dark matter - particles moving at relativistic speeds. However, the concept of temperature of a substance depends on interaction with other matter, and we don't know much about how much dark matter interacts with itself or with normal matter. Presumably it interacts enough to be cooled to the temperature of the 3K background radiation, but possibly does not interact enough with normal matter to be substantially warmed by it.
 
Even without interactions, I think that the stretching of space causes each DM particle to lose momentum (WRT the comoving frame) over time. Thus, they do cool.
 

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