How many neutrinos are in the universe?

Answer 1

There should be in excess of #10^79# neutrinos in the Universe.

Although the exact number of neutrinos in the universe is unknown, we can estimate it.

Let us first assume that neutrinos were either created in relatively small quantities or not at all during the Big Bang and that the only particles under consideration are protons and electrons; the amounts of antiprotons and electrons should be equal, but we are left with no explanation for the dominance of matter 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#.

The fusion process, in which a proton decays by the weak force into a neutron, a positron, and an electron neutrino, is the source of all neutrons in helium and heavier elements.

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

As antineutrinos are produced by some radioactive and fusion processes, where a neutron decays into a proton, an electron, and an electron antineutrino, this number is likely low. Neutrinos may have been created at the big bang.

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.
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Answer 2

Based on observations and calculations of the cosmic microwave background radiation and the universe's matter density, an estimate of the number of neutrinos in the universe is approximately 330 per cubic centimeter.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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