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In this short note we explain how to use the linear equation of motions tosimplify the third-order action for the cosmological fluctuations. No fieldredefinition is needed in this exact procedure which considerably limits therange of independent cubic operators, and hence of possible shapes of theprimordial bispectrum. We demonstrate this in the context of the most generalsingle-field scalar-tensor theory with second-order equations of motion, whosethird-order action has been calculated recently in arXiv:1107.2642 and1107.3917. In particular, we show that the three cubic operators initiallypointed out in these works as new compared to k-inflation can actually beexpressed in terms of standard k-inflationary operators.

On the redundancy of operators and the bispectrum in the most general second-order scalar-tensor theory