E-fold count for the natural-inflation cosine potential
= E-fold count for the natural-inflation cosine potential
For the cosine potential,
$$
N=\frac{2f^2}{M_{\rm Pl}^2}
\left[
\log\sin\frac{\phi_i}{2f}
-\log\sin\frac{\phi_f}{2f}
\right].
$$
= E-fold count for the natural-inflation cosine potential
For the cosine potential,
$$
N=\frac{2f^2}{M_{\rm Pl}^2}
\left[
\log\sin\frac{\phi_i}{2f}
-\log\sin\frac{\phi_f}{2f}
\right].
$$