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## Homework Statement

Cross-sections for weak interactions at an energy E increase with E as [itex]E^2[/itex]. Show that the rate of weak interactions in the early universe depends on the temperature T as [itex]\sigma_{wk} \propto T^5[/itex]

**2. The attempt at a solution**

The only formula I can find is

[tex]\sigma_{wk} = g_{wk}^2 \left[ \frac{k_B T}{(\bar{h} c)^2} \right]^2[/tex]

where [itex]g_{wk} \approx 1.4 \times 10^{49}[/itex] erg cm^3 is the weak interaction coupling constant.

I have no clue on how to proceed.