Kinetic mixing in scalar-tensor theories of gravity

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