Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity

TL;DR

This paper develops a method to analyze kinetic mixing in scalar-tensor gravity theories, classifying them into stirred and shaken types, and explores implications for stability, Einstein frame, and screening mechanisms.

Contribution

It introduces a Ricci curvature-free scalar field equation approach, providing new insights into the structure and classification of kinetic mixing in Horndeski and beyond theories.

Findings

Classified scalar-tensor theories into stirred and shaken categories.

Identified residual curvature coupling via the Weyl tensor in quartic Horndeski theories.

Showed generalized DBI Galileons belong to stirred theories.

Abstract

Kinetic mixing between the metric and scalar degrees of freedom is an essential ingredient in contemporary scalar-tensor theories. This often makes hard to understand their physical content, especially when derivative mixing is present, as it is the case for Horndeski action. In this work we develop a method that allows to write a Ricci curvature-free scalar field equation and discuss some of the advantages of such rephrasing in the study of stability issues in the presence of matter, the existence of an Einstein frame and the generalization of the disformal screening mechanism. For quartic Horndeski theories, such procedure leaves, in general, a residual coupling to curvature, given by the Weyl tensor. This gives rise to a binary classification of scalar-tensor theories into stirred theories, for which the curvature can be substituted for, and shaken theories for which a residual coupling to curvature remains. Quite remarkably, we have found that generalized DBI Galileons belong to the first class. Finally, we discuss kinetic mixing in quintic theories for which non-linear mixing terms appears and in the recently proposed theories beyond Horndeski which display a novel form of kinetic mixing, in which the field equation is sourced by derivatives of the energy-momentum tensor.