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P. Creminelli and M. Zaldarriaga, “Single field consistency relation for the 3-point function,” JCAP
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2008
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C. Cheung, P. Creminelli, A. L. Fitzpatrick, J. Kaplan and L. Senatore, “The Effective Field Theory of Inflation,” JHEP
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2008
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X. Chen, R. Easther and E. A. Lim, “Generation and Characterization of Large Non-Gaussianities in Single Field Inflation,” JCAP
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L. Boubekeur, P. Creminelli, J. Norena, F. Vernizzi, “Action approach to cosmological perturbations: the 2nd order metric in matter dominance,” JCAP
Original
2008
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Then

J. Khoury, P. J. Steinhardt, “Adiabatic Ekpyrosis: Scale-Invariant Curvature Perturbations from a Single Scalar Field in a Contracting Universe,” Phys. Rev. Lett
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2010
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2011
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2012

Conformal consistency relations for single-field inflation

Creminelli, Paolo, Noreña, Jorge, Simonović, Marko

Understand

We generalize the single-field consistency relations to capture not only the leading term in the squeezed limit---going as 1/q^3, where q is the small wavevector---but also the subleading one, going as 1/q^2.

This term, for an (n+1)-point function, is fixed in terms of the variation of the n-point function under a special conformal transformation; this parallels the fact that the 1/q^3 term is related with the scale dependence of the n-point function.
For the squeezed limit of the 3-point function, this conformal consistency relation implies that there are no terms going as 1/q^2.
We verify that the squeezed limit of the 4-point function is related to the conformal variation of the 3-point function both in the case of canonical slow-roll inflation and in models with reduced speed of sound.