Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 53 / 2 / i / a / Solution

Reducing the gravitational constant decreases $H$ at fixed temperature. The helium sensitivity to the expansion rate has two effects: weak interconversion persists to a lower freeze-out temperature, leaving fewer neutrons, and the universe takes longer to reach the deuterium-burning temperature, allowing more free-neutron decay after freeze-out. Both lower the helium-4 abundance. In particular $T_f\propto G^{1/6}$ and $t(T)\propto G^{-1/2}$.