Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 312 / 1 / i

Table of contents
- Solution i

Solution

Conformal time obeys

d t = a d η

, so

\dot{ϕ} = a^{- 1} ϕ^{'}

. Therefore

S_{int} = \frac{λ}{3 !} \int d^{3} x d η a (η) (ϕ^{'})^{3} .

For expanding de Sitter spacetime,

a = - 1/ (Hη)

with

- \infty < η < 0

.

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