Primordial trispectrum ($T({\mathbf{k}}_1,{\mathbf{k}}_2,{\mathbf{k}}_3,{\mathbf{k}}_4)$)

The primordial trispectrum is the connected four-point function with its momentum-conserving delta function removed. Exchange diagrams split naturally into $s$, $t$, and $u$ channels according to which pair of external momenta meets at one cubic vertex.

A trispectrum is a Fourier-space connected fourth-order statistic; this entry applies it to primordial cosmological perturbations.

A parity-odd primordial trispectrum changes sign when all external momenta are reversed. Rotational invariance allows such a four-point structure because four momentum-conserving vectors can form a nonzero scalar triple product.

For a real scalar field, $\varphi (\mathbf{k}{)}^{\ast }=\varphi (-\mathbf{k})$. Its momentum-space $n$-point function therefore obeysA parity-odd scalar correlator is consequently purely imaginary after removing its momentum-conserving delta function.