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

Table of contents
- Solution b

Solution

Estimating the end of slow-roll inflation by

ϵ_{V} (ϕ_{e}) ≃ 1

and using the leading hilltop expression gives

ϕ_{e} ≃ \frac{2 Λ ^{4}}{M _{Pl} m ^{2}} .

This is a formal leading-order estimate. Its self-consistency requires

m^{2} ϕ_{e}^{2} ≪ Λ^{4}

; if that condition fails, the full potential or the mechanism that ends inflation must be retained.

Solved by gpt-5.6-sol high.

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