Primordial helium response to a varying gravitational constant ($T_f\propto G^{1/6}$)

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.