Stealth dark energy in scordatura DHOST theory. (arXiv:2009.11606v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Gorji_M/0/1/0/all/0/1">Mohammad Ali Gorji</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Motohashi_H/0/1/0/all/0/1">Hayato Motohashi</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Mukohyama_S/0/1/0/all/0/1">Shinji Mukohyama</a>
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.
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.
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