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Stealth dark energy in scordatura DHOST theory. (English) Zbl 1485.83046

Summary: A stealth de Sitter solution in scalar-tensor theories has an exact de Sitter background metric and a nontrivial scalar field profile. Recently, in the context of Degenerate Higher-Order Scalar-Tensor (DHOST) theories it was shown that stealth de Sitter solutions suffer from either infinite strong coupling or gradient instability for scalar field perturbations. The sound speed squared is either vanishing or negative. In the first case, the strong coupling scale is zero and thus lower than the energy scale of any physical phenomena. From the viewpoint of effective field theory, this issue is naturally resolved by introducing a controlled detuning of the degeneracy condition dubbed scordatura, recovering a version of ghost condensation. In this paper we construct a viable dark energy model in the scordatura DHOST theory based on a stealth cosmological solution, in which the metric is the same as in the standard \(\Lambda\)CDM model and the scalar field profile is linearly time-dependent. We show that the scordatura mechanism resolves the strong coupling and gradient instability. Further, we find that the scordatura is also necessary to make the quasi-static limit well-defined, which implies that the subhorizon observables are inevitably affected by the scordatura. We derive the effective gravitational coupling and the correction to the friction term for the subhorizon evolution of the linear dark matter energy density contrast as well as the Weyl potential and the gravitational slip parameter. In the absence of the scordatura, the quasi-static approximation would break down at all scales around stealth cosmological solutions even if the issue of the infinite strong coupling is unjustly disregarded. Therefore previous estimations of the subhorizon evolution of matter density contrast in modified gravity in the literature need to be revisited by taking into account the scordatura effect.

MSC:

83C56 Dark matter and dark energy
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83F05 Relativistic cosmology
35B20 Perturbations in context of PDEs
83C15 Exact solutions to problems in general relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
76E20 Stability and instability of geophysical and astrophysical flows
76Q05 Hydro- and aero-acoustics
83C25 Approximation procedures, weak fields in general relativity and gravitational theory

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