Solution
= Solution
The <slow-roll approximation> assumes
$$
\dot\phi^2\ll V(\phi),
\qquad
|\ddot\phi|\ll3H|\dot\phi|.
$$
The first condition makes the energy density potential dominated, and the second neglects inertial acceleration relative to Hubble friction. The scalar and Friedmann equations reduce to
$$
\boxed{3H\dot\phi\simeq-V'(\phi)},
\qquad
\boxed{H^2\simeq\frac{8\pi G}{3c^2}V(\phi)}.
$$