Thread: Re: The end of inflation View Single Post


In article , Charles Francis wrote: >You gave a figure for energy in neutrinos, which I assume was based on >the neutrino having zero mass, but do we have any idea how much missing >matter there may be in cold neutrinos if neutrinos have mass? You're right: the number I quoted was assuming massless neutrinos. Theoretically, the story should go like this. If neutrinos are massless, they should have a thermal distribution with a temperature of about 2 K today. That corresponds to an energy of $kT =$ .2 meV. So any neutrino species with a mass much less than that is effectively massless. What about neutrino species with masses more than that? They were still ultrarelativistic (so effectively massless) in the early Universe when the neutrino background formed, so the number density of such neutrinos (averaged over the whole Universe) should be the same as in the massless case. That number density works out to be something like 100 particles $/ cm^3$ in each species. (That's just an order of magnitude. Kolb & Turner's "The Early Universe," among others, would give the exact figure.) Any neutrino species with a mass above an meV or so would be nonrelativistic today, so its energy would essentially just be its rest energy. So if you have a favorite value for the mass of a neutrino species, just multiply that by about 100 $/ cm^3$ to get the density in those particles. If you want to convert that to an $\Omega,$ divide by the critical density, which is about $10^4 eV/cm^3$. Incidentally, if neutrinos are massive enough to be nonrelativistic, then they clump gravitationally. So the density of such particles in our galaxy would be more than that average value over the whole Universe. $$-Ted$$ -- [E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]