Higher-derivative operators and effective field theory for general scalar-tensor theories

TL;DR

This paper examines when higher-derivative operators are necessary in the effective field theory of scalar-tensor theories, especially Horndeski models, and how they can be simplified for practical use in cosmology.

Contribution

It clarifies the conditions under which higher-derivative operators can be omitted or reduced in scalar-tensor effective field theories, using various techniques including field redefinitions.

Findings

Higher-derivative operators can often be recast into second-order forms.

Techniques like reduction of order simplify the effective field theory.

The work aids in applying EFT methods to cosmological models.

Abstract

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order operators only, and demonstrate this using several different techniques, such as reduction of order and explicit field redefinitions. These methods are applied, in particular, to the much-studied Horndeski theories. The goal is to clarify the application of effective field theory techniques in the context of popular cosmological models, and to explicitly demonstrate how and when higher-derivative operators can be cast into lower-derivative forms suitable for numerical solution techniques.