= Cubic time-derivative curvature bispectrum
{title2=$H_{\rm int}\propto\dot\zeta^3$}
Put $C=\epsilon+1-c_s^2$. For constant $H,\epsilon,c_s>0$ and cubic interaction $H_{\rm int}=-M_{\rm Pl}^2\int d^3x\,a^3\epsilon C\dot\zeta^3/(Hc_s^2)$, the <Bunch-Davies vacuum> modes $u_k=H(1+ikc_s\tau)e^{-ikc_s\tau}/\sqrt{4\epsilon M_{\rm Pl}^2c_sk^3}$ give
$$
B(k_1,k_2,k_3)=\frac{3H^4C}{8\epsilon^2M_{\rm Pl}^4c_s^2k_1k_2k_3(k_1+k_2+k_3)^3}.
$$
To derive this <primordial bispectrum>, transform $dt=a\,d\tau$, $\dot\zeta=\zeta'/a$, use the six connected <Wick contractions>, and integrate $\int_{-\infty(1-i0)}^0\tau^2e^{ic_s(k_1+k_2+k_3)\tau}\,d\tau=2i/[c_s(k_1+k_2+k_3)]^3$ in the <in-in formalism>. The normalized equilateral amplitude is $B(k,k,k)/P(k)^2=2C/9$; raw inverse powers of $c_s$ must not be confused with normalized <primordial non-Gaussianity>.
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