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

A late-time connected four-point function of a scale-invariant field in three spatial dimensions, after removing its momentum-conserving delta function, must obeyIn both contributions, $s/(k_1{k}_2{k}_3{k}_4)$ scales as ${\Lambda }^{-3}$ and every energy-denominator term scales as ${\Lambda }^{-6}$. Hence the complete $s$-channel primordial trispectrum scales as ${\Lambda }^{-9}$, as required by scale invariance.