Avoidance of Strong Coupling in General Relativity Solutions with a Timelike Scalar Profile in a Class of Ghost-Free Scalar-Tensor Theories

Modified gravity theories can accommodate exact solutions, for which the metric has the same form asthe one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is thatperturbations 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 theframework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a waythat higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect isbuilt-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 spacelikehypersurface. We also clarify how this nonpropagating mode, i.e., theshadowymode shows up at thenonlinear level.

Automated summary

In modified gravity theories, the strong coupling problem of stealth solutions can be avoided with the use of U-DHOST theories. Additionally, the existence of a nonpropagating mode in U-DHOST theories is clarified.