Estimating the end of <slow-roll inflation> by $\epsilon_V(\phi_e)\simeq1$ and using the leading hilltop expression gives
$$
\boxed{\phi_e\simeq
\frac{\sqrt2\,\Lambda^4}{M_{\rm Pl}m^2}}.
$$
This is a formal leading-order estimate. Its self-consistency requires $m^2\phi_e^2\ll\Lambda^4$; if that condition fails, the full potential or the mechanism that ends inflation must be retained.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 310 / 2 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-310/2/b/solution