= Primordial helium response to a varying gravitational constant
{title2=$T_f\propto G^{1/6}$}
If the <Friedmann equation> remains approximately $H^2=8\pi G\rho/3$, <radiation domination> and fixed weak microphysics give $H\propto\sqrt G\,T^2$ and a neutron-proton conversion rate proportional to $T^5$. <Cosmological weak freeze-out> then occurs at $T_f\propto G^{1/6}$. Increasing $G$ during this era raises the <neutron-to-proton ratio> at freeze-out and shortens the time for <free-neutron decay after freeze-out>. Both increase the <primordial helium mass fraction> when <neutron-limited helium synthesis> remains efficient. Arbitrary variation of $G$ over time requires its history and the full gravitational field equations; this scaling is a controlled background approximation, rather than a complete model of gravity with arbitrary time dependence.
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