Built-in scordatura in U-DHOST

TL;DR

This paper demonstrates that U-DHOST theories inherently incorporate a built-in scordatura mechanism that avoids strong coupling issues in stealth solutions by ensuring nonpropagating Ostrogradsky modes, thus improving the viability of modified gravity models.

Contribution

It introduces the concept of built-in scordatura in U-DHOST theories, showing how it prevents strong coupling in stealth solutions by controlling Ostrogradsky modes.

Findings

U-DHOST theories partially break degeneracy to include built-in scordatura.

Ostrogradsky modes in U-DHOST do not propagate and satisfy elliptic equations.

Nonpropagating modes appear at the nonlinear level as shadowy modes.

Abstract

Modified gravity theories can accommodate exact solutions, for which the metric has the same form as the one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is that perturbations around them exhibit strong coupling when the solutions are realized in degenerate higher-order scalar-tensor theories. We show that the strong coupling problem can be circumvented in the framework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a way that higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect is built-in in U-DHOST theories in general. There is an apparent Ostrogradsky mode in U-DHOST theories, but it does not propagate as it satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface. We also clarify how this nonpropagating mode, i.e., the "shadowy" mode shows up at the nonlinear level.