Cubic curvature action for a P(X, phi) scalar field

In the limit where scalar field fluctuations dominate metric fluctuations, put $\zeta =-H\delta \varphi /\dot{\bar{\varphi }}$ and neglect derivatives of slowly varying background coefficients. Splitting $\delta X=\delta X_1+\delta X_2$ givesThe cubic terms $P_{XX}\delta X_1\delta X_2+P_{XXX}\delta X_1^3/6$ therefore yieldThe expression before factoring remains well-defined when $P_{XX}=0$. These interactions can generate substantial primordial non-Gaussianity when the Sound speed of a P(X, phi) scalar perturbation is small.