How many neutrinos are in the universe?

We can't be sure for certain how many neutrinos there are in the Universe, but we can make an estimate.

First of all let's assume that there were relatively few or no neutrinos created in the big bang. The only particles being considered are protons and electrons. There should be equal amounts of antiprotons and electrons, but we have no explanation as to why matter dominated over antimatter.

Estimates put the number of atoms in the Universe at #10^80# in the observable Universe. Actually estimates vary from #10^78# to #10^82#.

About 75% of the mass of matter is Hydrogen and most of the remaining 25% of the mass is Helium. Heavier elements are relatively rare. Given that Helium has two protons and two neutrons, we can estimate the number of neutrons to be about 10% of the number of protons or a number of #10^79#.

All of the neutrons in Helium and heavier elements were created as part of the fusion process where a proton decays by the weak force into a neutron, a positron and an electron neutrino.

So, as creating a neutron also creates a neutrino, they should occur in similar numbers at about #10^79#.

This figure is probably on the low side as there may have been neutrinos created at the big bang. Also, antineutrinos are created by some radioactive and fusion processes, where a neutron decays into a proton, an electron and an electron antineutrino.

If an neutrino and an antineutrino of the same flavour collide they will annihilate each other. As neutrinos don't interact much such collisions will be quite infrequent. Also, the neutrino-antineutrino annihilation is a weak force process where they become a #Z^0# boson. The Z decays rapidly. Depending on the neutrino energy the Z can decay into two photons, but it is more likely to decay back into a neutrino-antineutrino pair.

So, in summary the number of neutrinos is in the order of #10^79# to within two orders of magnitude.