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

TL;DR

This paper simplifies the third-order action for cosmological fluctuations in the most general second-order scalar-tensor theories by using equations of motion, reducing the independent operators and clarifying the bispectrum's shape.

Contribution

It introduces an exact method to eliminate redundant operators in the third-order action without field redefinitions in scalar-tensor theories.

Findings

Reduces the number of independent cubic operators in the action.

Shows that previously identified new operators are expressible in terms of standard ones.

Clarifies the shape of the primordial bispectrum in these theories.

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.