Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 312 / 3 / iii / a

Write a filled vertex with $n$ incoming linear fields for the $n$th-order peculiar-velocity divergence. Gaussian initial conditions require every linear field to be paired. Through sixth order in the linear density there are exactly five connected topologies: the tree diagram $B_{211}$ and the one-loop triangle $B_{222}$, vertex-correction diagram $B_{321}^I$, propagator-correction diagram $B_{321}^{II}$, and four-leg diagram $B_{411}$. These are the five diagrams of the one-loop matter bispectrum.