A late-time connected four-point function of a scale-invariant field in three spatial dimensions, after removing its momentum-conserving delta function, must obey
$$
B_4(\Lambda\mathbf k_1,\ldots,\Lambda\mathbf k_4)
=\Lambda^{-9}B_4(\mathbf k_1,\ldots,\mathbf k_4).
$$
In both contributions, $s/(k_1k_2k_3k_4)$ 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.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-312/1/v/solution