= Potential and Hubble slow-roll parameter relation
{title2=$\eta\simeq4\epsilon_V-2\eta_V$}
For a canonical <inflaton> under the <slow-roll approximation>, $\dot\phi/H\simeq-M_{\rm Pl}^2V'/V$ and $\epsilon\simeq\epsilon_V=(M_{\rm Pl}^2/2)(V'/V)^2$. Differentiating $\log\epsilon_V$ along this trajectory gives
$$
\eta\simeq2\left(\frac{V''}{V'}-\frac{V'}V\right)\frac{\dot\phi}{H}=4\epsilon_V-2\eta_V.
$$
Here $\eta=d\log\epsilon/d\log a$, not the alternate convention $-\ddot\phi/(H\dot\phi)$. The logarithmic definition requires $\epsilon>0$; exact de Sitter expansion is treated as a limit.
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