# Dark Matter Abundance and Being a Cold Relic

I was reading Longair its stated that,

"An important conclusion was that, if dark matter particles were as common as neutrinos and photons,their rest mass energies could not be much greater than $$10eV$$, or the present density of the Universe would exceed the critical mass density $$Ω_0 = 1$$. Therefore, there would have to be some suppression mechanism to ensure that the massive particles were much less common than the photons and neutrinos at the present day.

There is a natural way in which this can occur if the decoupling of the WIMPs from thermal equilibrium took place after they had become non-relativistic, that is, the decoupling took place after the epoch at which $$kT ∼ m_Xc^22$$, where $$m_X$$ is the mass of the WIMP."

I did not understand this conclusion. What is the relationship between having less DM particle and being cold relic ?

When the dark matter particles were relativistic, their number density goes like $$n_{rel} \sim T^3$$. After becoming non-relativistic, they are exponentially suppressed $$n_{non-rel} \sim T^{3/2} e^{-m/T}$$. (These are found by solving the phase space distributions for species in kinetic equilibrium).