We have to calculate the minimum temperature of the universe for the photons to produce pairs; and find the age of the universe when it had this temperature.

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The rest mass energy of is 140 MeV.

For photons to produce pairs, the photon energy kT must be at least as large as the rest energy of a pion that is 140 MeV. Therefore,

The relation between the temperature and age of the universe is

Therefore, the age of the universe, when its temperature was , was