Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 312 / 2 / v / Solution

Substitution of $\delta N=C\phi$ and conversion to conformal time turn the interaction intoTreat $C$ and $H$ as constant at leading slow-roll order and use the massless de Sitter modeFor $K=k_1+k_2+k_3$, the in-in formalism time integral at a vertex with leg $i$ undifferentiated is proportional toSumming the three choices of undifferentiated leg gives the primordial bispectrumThe sign follows from the interaction sign displayed in the question and $H_I=-L_{\mathrm{int}}$ at this order.