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

Abstract

In this short note we explain how to use the linear equation of motions to simplify the third-order action for the cosmological fluctuations. No field redefinition is needed in this exact procedure which considerably limits the range of independent cubic operators, and hence of possible shapes of the primordial bispectrum. We demonstrate this in the context of the most general single-field scalar-tensor theory with second-order equations of motion, whose third-order action has been calculated recently in arXiv:1107.2642 and 1107.3917. In particular, we show that the three cubic operators initially pointed out in these works as new compared to k-inflation can actually be expressed in terms of standard k-inflationary operators.

9 pages. Wordings changed; matches version published in JCAP

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• Inflationary signatures of single-field models beyond slow-roll
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• No time to derive: unraveling total time derivatives in in-in perturbation theory
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• Non-Canonical Inflation in Supergravity
• A Modal Approach to the Numerical Calculation of Primordial non-Gaussianities
• Why does the effective field theory of inflation work?
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• Metric-Affine Formalism of Higher Derivative Scalar Fields in Cosmology
• Constraints on Single-Field Inflation
• Lowering the self-coupling of the scalar field in a generalized Higgs inflation
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• Loops in inflation with strongly non-geodesic motion
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