= Derivative-cubic coefficient of a noncanonical scalar
{title2=$C=-\frac{a^3}{H^3}(2\bar X^2P_{,XX}+\frac43\bar X^3P_{,XXX})$}
Neglect metric fluctuations and derivatives of $\dot{\bar\phi}/H$, so $\delta X_1=-2\bar X\dot\zeta/H$ and $\delta X_2=\bar X[\dot\zeta^2-a^{-2}(\nabla\zeta)^2]/H^2$. The coefficient of $\dot\zeta^3$ in the cosmic-time action is $C=-a^3[2\bar X^2P_{,XX}+(4/3)\bar X^3P_{,XXX}]/H^3$. This unfactored form is valid even when $P_{,XX}=0$ and a factored ratio would be undefined.
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