Nonlinear definition of the shadowy mode in higher-order scalar-tensor theories

TL;DR

This paper investigates U-DHOST higher-order scalar-tensor theories, revealing that the so-called 'shadowy' mode is non-propagating and can be described by an elliptic equation, clarifying its treatment at linear and nonlinear levels.

Contribution

It introduces a nonlinear framework for understanding the shadowy mode in U-DHOST theories, showing it satisfies an elliptic equation and does not propagate.

Findings

The shadowy mode is governed by an elliptic differential equation.

The mode does not propagate in generic coordinate systems.

The paper clarifies how to treat the shadowy mode at different levels.

Abstract

We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode in a generic coordinate system. We show that the extra mode satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface, and hence it does not propagate. We clarify how to treat this "shadowy" mode at both the linear and the nonlinear levels.