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Modified gravity theories can accommodate exact solutions, for which the metric has the same form as the one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is that perturbations around them exhibit strong coupling when the solutions are realized in degenerate higher-order scalar-tensor theories. We show that the strong coupling problem can be circumvented in the framework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a way that higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect is built-in in U-DHOST theories in general. There is an apparent Ostrogradsky mode in U-DHOST theories, but it does not propagate as it satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface. We also clarify how this nonpropagating mode, i.e., the "shadowy" mode shows up at the nonlinear level.

We present results from a controlled numerical experiment investigating the effect of stellar density gas on the coalescence of binary black holes (BBHs) and the resulting gravitational waves (GWs). This investigation is motivated by the proposed stellar core fragmentation scenario for BBH formation and the associated possibility of an electromagnetic counterpart to a BBH GW event. We employ full numerical relativity coupled with general-relativistic hydrodynamics and set up a 30+30  M_{⊙} BBH (motivated by GW150914) inside gas with realistic stellar densities. Our results show that at densities ρ≳10^{6}-10^{7}  g cm^{-3} dynamical friction between the BHs and gas changes the coalescence dynamics and the GW signal in an unmistakable way. We show that for GW150914, LIGO observations appear to rule out BBH coalescence inside stellar gas of ρ≳10^{7}  g cm^{-3}. Typical densities in the collapsing cores of massive stars are in excess of this density. This excludes the fragmentation scenario for the formation of GW150914.

The standard cold dark matter model with a cosmological constant (Λ-CDM) predicts a growth of structures which tends to be higher than the values of redshift space distortion (RSD) measurements if the cosmological parameters are fixed by the cosmic microwave background data. In this Letter, we point out that this discrepancy can be resolved or understood if we assume that the graviton has a small but nonzero mass. In the context of the minimal theory of massive gravity (MTMG), due to infrared Lorentz violations measurable only at present cosmological scales, the graviton acquires a mass without being haunted by unwanted extra degrees of freedom. While the so-called self-accelerating branch of cosmological solutions in the MTMG has the same phenomenology for the background as well as the scalar- and vector-type linear perturbations as the ΛCDM in general relativity (GR), it is possible to choose another branch so that the background is the same as that in GR, but the evolution of matter perturbations gets modified by the graviton mass. In studying the fit of such modified dynamics to the above-mentioned RSD measurements, we find that the ΛCDM model is less probable than the MTMG by 2 orders of magnitude. With the help of the cross-correlation between the integrated Sachs-Wolfe effect and the large-scale structure, the data also pin down the graviton mass squared around μ^{2}≈-(3×10^{-33}  eV)^{2}, which is consistent with the latest bound |μ^{2}|<(1.2×10^{-22}  eV)^{2} set by the recent LIGO observation.

We argue that all homogeneous and isotropic solutions in nonlinear massive gravity are unstable. For this purpose, we study the propagating modes on a Bianchi type-I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. This ghost mode is interpreted as a leading nonlinear perturbation around a homogeneous and isotropic background.

We study the cosmology of a covariant scalar field respecting a Galilean symmetry in flat space-time. We show the existence of a tracker solution that finally approaches a de Sitter fixed point responsible for cosmic acceleration today. The viable region of model parameters is clarified by deriving conditions under which ghosts and Laplacian instabilities of scalar and tensor perturbations are absent. The field equation of state exhibits a peculiar phantomlike behavior along the tracker, which allows a possibility to observationally distinguish the Galileon gravity from the cold dark matter model with a cosmological constant.

Over the past decade, f ( R ) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f ( R ) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.