"Shadowy" modes in Higher-Order Scalar-Tensor theories

TL;DR

This paper classifies higher-order scalar-tensor theories that are degenerate in certain gauges, revealing a non-propagating 'shadowy' mode that can be eliminated through boundary conditions, thus clarifying stability issues.

Contribution

It provides a comprehensive classification of U-degenerate theories and analyzes the nature of shadowy modes in these theories, extending understanding of their stability.

Findings

Shadowy modes are non-propagating and can be eliminated with boundary conditions.

U-degenerate theories include a class of higher-order scalar-tensor models.

Proper boundary conditions remove apparent instabilities.

Abstract

We consider Higher-Order Scalar-Tensor theories which appear degenerate when restricted to the unitary gauge but are not degenerate in an arbitrary gauge. We dub them U-degenerate theories. We provide a full classification of theories that are either DHOST or U-degenerate and that are quadratic in second derivatives of the scalar field, and discuss its extension to cubic and higher order theories. Working with a simple example of U-degenerate theory, we find that, for configurations in which the scalar field gradient is time-like, the apparent extra mode in such a theory can be understood as a generalized instantaneous, or "shadowy" mode, which does not propagate. Appropriate boundary conditions, required by the elliptic nature of part of the equations of motion, lead to the elimination of the apparent instability associated with this extra mode.