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

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-Lema\^{i}tre-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 $w_{\rm DE}$ is equivalent to $-1$ or varies in time. We find that the deviation from the value $w_{\rm DE}=-1$ 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 $w_{\rm DE}>-1$ and $w_{\rm DE}<-1$. We also generally obtain the effective gravitational coupling $G_{\rm eff}$ 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 $G_{\rm eff}$ and $\eta_s$ are similar to those in general relativity for scalar perturbations deep inside the sound horizon.Comment: 26 pages, 2 figue

Cosmology in doubly coupled massive gravity: constraints from SNIa, BAO and CMB

Massive gravity in the presence of doubly coupled matter field via en effective composite metric yields an accelerated expansion of the universe. It has been recently shown that the model admits stable de Sitter attractor solutions and could be used as a dark energy model. In this work, we perform a first analysis of the constraints imposed by the SNIa, BAO and CMB data on the massive gravity model with the effective composite metric and show that all the background observations are mutually compatible at the one sigma level with the model.Comment: 7 pages, 4 figure