Question

One of the reasons neutrons stopped forming in the earlier universe was the annihila- tion of electron-positron pairs. When the temperature became too low, the electron- positron pairs could not be replaced by pair production. Since this then removed the supply of electrons that could combine with protons to form neutrons, the neutrons decayed into protons until the universe cooled down enough for the protons and neu- trons to combine to form deuterium nuclei.

a. By setting the characteristic thermal energy of a photon, kT, equal to the rest energy of an electron-positron pair, estimate the temperature below which an annihi- lated pair will not readily be replaced.

b. What was the age of the universe when it was the temperature calculated in part (a)?

c. What was the density of the universe at this time and temperature? How many Earths (or fraction of Earth) can fit inside a km cube?

Answer 1