Weakly-coupled stealth solution in scordatura degenerate theory

TL;DR

This paper investigates the strong coupling issues of perturbations around stealth solutions in scalar-tensor theories and proposes a controlled detuning, called scordatura, to maintain weak coupling without altering astrophysical properties.

Contribution

It introduces the concept of scordatura, a controlled detuning of degeneracy, to resolve strong coupling problems in stealth solutions of degenerate theories.

Findings

Effective field theory exhibits a universal dispersion relation with positive alpha.

Scordatura detuning renders perturbations weakly coupled up to the background scalar field scale.

The approach preserves astrophysical properties of stealth solutions in degenerate theories.

Abstract

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.