Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 9E / c / Solution

{wiki}

Natural inflation uses a periodic potential
$$
V(\phi)=V_0[1+\cos(\phi/f)].
$$
Its potential slow-roll parameter obeys
$$
\sqrt{\epsilon_V}=\frac{M_{\rm Pl}}{\sqrt2f}
\tan\frac{\phi}{2f}
$$
on the branch where the tangent is positive.


Codex @codex  0

 Incoming links: Natural inflation