Weakly-coupled stealth solution in scordatura degenerate theory

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 ω 2 = αk 4 /M 2 , where M is a mass scale characterizing the background scalar field and α is a dimensionless constant. Provided that α 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 α = 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.

Stealth black holes in shift symmetric kinetic gravity braiding

“…We note that this conclusion has been reached before within the broader class of DHOST theories [31,33,34] and from the EFT perspective [36,60] 5 . This paper complements the existing literature by directly obtaining the conclusion directly within shift symmetric KGB and by working with the field equations instead of the second-order action.…”

“…It is important to recognize four recent works which have shed light to the issue of strong coupling of perturbations of stealth black holes in scalar-tensor theories [29,34,37,60]. In Ref.…”

“…In Ref. [60], it was proposed that the strong coupling problem can be resolved by introducing a heavy Ostrogradsky ghost that would not be triggered or rendered observable for scales below the EFT cutoff. This lead to theories -dubbed scordatura degenerate theories -which relaxes the degeneracy conditions previously imposed in DHOST theories to avoid the Ostrogradsky instability.…”

Disforming the Kerr metric

“…Note that stealth black holes were found to have a problem with perturbations, namely the scalar mode becomes non-dynamical on such background solutions, which is related to strong coupling[39,40]. However, it has been argued in[48] that a small detuning of the degeneracy condition for the theory can be used to solve this problem.…”

On quasinormal frequencies of black hole perturbations with an external source

“…There, the matter field can be non-minimally coupled to the curvature sector, and therefore, one might expect the resultant master equations in the time-domain to become inhomogeneous. As an example, the degenerate higher-order scalar-tensor (DHOST) theory [7,11,12] may admit "stealth" solutions [13][14][15][16]. The latter does not influence the background metric due to its vanishing energymomentum tensor [17].…”