The reason that massive neutrinos were considered as a candidate for solving the

Question

The reason that massive neutrinos were considered as a candidate for solving the missing mass problem is that, at the conclusion of the lepton era, the universe contained about equal numbers of photons and neutrinos. They are still here, for the most part. The former can be observed and their density is measured to be about 500 photons/cm^3, thus, there must be about that number density of neutrinos in the universe, too. If neutrinos have a onzero mass and if the cosmological expansion has reduced their average speed so that their energy is now primarily mass, what would be the individual neutrino mass (in eV/c^2) necessary to account for the missing mass of the universe? Recall that the observed mass of the stars and galaxies, accounts for about 4 percent of the mass of the universe.

Also, if anyone can tell me how to ask a question from my textbook (which is registered) so that it appears for the textbook instead of as an independant question, I feel like that could help other people too. Thanks! (This is question 5, chapter 13, of Modern Physics by Paul Allen Tipler)

Explanation / Answer

the mass of the universe is about 3E54 kg 96% of that is 2.88E54 kg. in eV/c^2 that is 1.6E90 ev/c^2. Now lets estimate the number of neutrinos the volume of the universe is about 3.5E80 cubic meters or 3.5E86 cm^3 that means there are 3.5E86* 500=1.75E89 neutrinos so the mass of each neutrinos would be 1.6E90/1.75E89=9.14 ev/c^2

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