Monomial slow-roll e-fold count
= Monomial slow-roll e-fold count
For $V(\phi)=\lambda\phi^n/n$ under the stated Cambridge Tripos normalization,
$$
N_e=\frac{4\pi G}{c^4n}
(\phi_i^2-\phi_f^2).
$$
If slow roll ends by kinetic-potential equality, then
$$
\phi_f^2\simeq\frac{n^2c^4}{48\pi G},
\qquad
N_e\simeq\frac n{12}
\left[\left(\frac{\phi_i}{\phi_f}\right)^2-1\right].
$$