First Hubble slow-roll parameter ($ϵ$)

The first Hubble slow-roll parameter isFor a canonical inflaton, $ϵ={\dot{\varphi }}^2/(2M_{\mathrm{Pl}}^2{H}^2)\ge 0$.

For flat expansion with a canonical scalar and no additional fluid, differentiating the Friedmann equation gives $\dot{H}=-4\pi G{\dot{\varphi }}^2\le 0$. Expansion can still accelerate if $-\dot{H}/H^2<1$. Equality at an isolated turning point does not imply eternal de Sitter expansion.