Spatial-gradient cubic curvature bispectrum ($H_{\mathrm{int}}=g\int d^{3}xa\zeta (\partial \zeta {)}^2$)

With cosmic-time interaction coefficient $g$, constant $H,ϵ,c_s$, and modes whose positive-frequency part is $H(1+ik{c}_s\tau )e^{-ik{c}_s\tau }/\sqrt{4ϵc_s{k}^3}$ in units $M_p=1$, two Wick contractions per differentiated pair and the late-time scalar gradient vertex integral giveHere $⟨{\zeta }^3{⟩}_c=(2\pi {)}^3{\delta }^3(\sum {\mathbf{k}}_i)B$. The extra factor $a$ in $dt=ad\tau$ must be included. A positive $g$ yields a negative bispectrum in an equilateral bispectrum configuration; changing the sign of the interaction changes the sign of $B$.