Dark energy survivals in massive gravity after GW170817: SO(3) invariant

Abstract

The recent detection of the gravitational wave signal GW170817 together with an electromagnetic counterpart GRB 170817A from the merger of two neutron stars puts a stringent bound on the tensor propagation speed. This constraint can be automatically satisfied in the framework of massive gravity. In this work we consider a general $SO(3)$-invariant massive gravity with five propagating degrees of freedom and derive the conditions for the absence of ghosts and Laplacian instabilities in the presence of a matter perfect fluid on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological background. The graviton potential containing the dependence of three-dimensional metrics and a fiducial metric coupled to a temporal scalar field gives rise to a scenario of the late-time cosmic acceleration in which the dark energy equation of state $w_{\mathrm{DE}}$ is equivalent to $-1$ or varies in time. We find that the deviation from the value $w_{\mathrm{DE}}=-1$ provides important contributions to the quantities associated with the stability conditions of tensor, vector, and scalar perturbations. In concrete models, we study the dynamics of dark energy arising from the graviton potential and show that there exist viable parameter spaces in which neither ghosts nor Laplacian instabilities are present for both $w_{\mathrm{DE}}>-1$ and $w_{\mathrm{DE}}<-1$. We also generally obtain the effective gravitational coupling $G_{\mathrm{eff}}$ with non-relativistic matter as well as the gravitational slip parameter ${\eta }_s$ associated with the observations of large-scale structures and weak lensing. We show that, apart from a specific case, the two quantities $G_{\mathrm{eff}}$ and ${\eta }_s$ are similar to those in general relativity for scalar perturbations deep inside the sound horizon.

26 pages, 2 figues

References in corpus (24)

• Dynamics of dark energy
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Resummation of Massive Gravity
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Beyond the Cosmological Standard Model
• Covariant Galileon
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Measuring the dark side (with weak lensing)
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Massive gravity: nonlinear instability of the homogeneous and isotropic universe
• Cosmic Acceleration and the Helicity-0 Graviton
• On couplings to matter in massive (bi-)gravity
• Ghosts & Matter Couplings in Massive (bi-&multi-)Gravity
• Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories
• Self-accelerating Massive Gravity: Exact solutions for any isotropic matter distribution
• Lorentz Breaking Massive Gravity in Curved Space
• Cosmology of the proxy theory to massive gravity
• Cosmological perturbations in massive gravity with doubly coupled matter
• Quantum corrections in massive bigravity and new effective composite metrics
• Massive gravity and structure formation
• Observational signatures of the parametric amplification of gravitational waves during reheating after inflation
• Suppression of matter couplings with a vector field in generalized Proca theories
• Cosmology in rotation-invariant massive gravity with non-trivial fiducial metric

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