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Along cosmological horizon exit $k\propto aH$, differentiation gives $d\log k/d\log a=1-{ϵ}_H$, where ${ϵ}_H=-\dot{H}/H^2$. The chain rule gives the first expression. In reduced Planck units, the slow-roll equations $3H\dot{\varphi }\simeq -V^{\prime }$ 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.

Planck units use fundamental constants to set natural units of mass, length and time. The displayed convention sets the ordinary Planck mass to one. The related reduced Planck units convention instead normalizes the reduced Planck mass.