Built-in scordatura in U-DHOST

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.

6 pages, 1 figure

References in corpus (13)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Quantum Gravity at a Lifshitz Point
• Horndeski theory and beyond: a review
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• Unifying framework for scalar-tensor theories of gravity
• Third order equations of motion and the Ostrogradsky instability
• Hamiltonian analysis of spatially covariant gravity
• Extended mimetic gravity: Hamiltonian analysis and gradient instabilities
• Fundamental theorem on gauge fixing at the action level
• Weakly-coupled stealth solution in scordatura degenerate theory
• Invertible disformal transformations with higher derivatives
• Black hole perturbations in DHOST theories: Master variables, gradient instability, and strong coupling

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