= Horizon-exit logarithmic derivative in slow roll
{title2=$\frac d{d\log k}=\frac1{1-\epsilon_H}\frac{\dot\phi}H\frac d{d\phi}\simeq-\frac{V'}V\frac d{d\phi}$}
Along <cosmological horizon exit> $k\propto aH$, differentiation gives $d\log k/d\log a=1-\epsilon_H$, where $\epsilon_H=-\dot H/H^2$. The <chain rule> gives the first expression. In <reduced Planck units>, the <slow-roll equations> $3H\dot\phi\simeq-V'$ and $3H^2\simeq V$ give the second expression to leading order. Applied to a quantity already of slow-roll order, the omitted factor changes the answer only at second order.
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