Weakly-coupled stealth solution in scordatura degenerate theory
  In scalar-tensor theories we revisit the issue of strong coupling of
perturbations around stealth solutions, i.e.\ backgrounds with the same forms
of the metric as in General Relativity but with non-trivial configurations of
the scalar field. The simplest among them is a stealth Minkowski (or de Sitter)
solution with a constant, timelike derivative of the scalar field, i.e.\ ghost
condensation. In the decoupling limit the effective field theory (EFT)
describing perturbations around the stealth Minkowski (or de Sitter) solution
shows the universal dispersion relation of the form $\omega^2 = \alpha
k^4/M^2$, where $M$ is a mass scale characterizing the background scalar field
and $\alpha$ is a dimensionless constant. Provided that $\alpha$ is positive
and of order unity, a simple scaling argument shows that the EFT is weakly
coupled all the way up to $M$. On the other hand, if the structure of the
underlining theory forces the perturbations to follow second-order equations of
motion then $\alpha=0$ and the dispersion relation loses dependence on the
spatial momentum. This not only explains the origin of the strong coupling
problem that was recently pointed out in a class of degenerate theories but
also provides a hint for a possible solution of the problem. We then argue that
a controlled detuning of the degeneracy condition, which we call scordatura,
renders the perturbations weakly coupled without changing the properties of the
stealth solutions of degenerate theories at astrophysical scales.
