Abstract
We present the cosmological analysis of the Gauss-Bonnet quasi-dilaton massive gravity theory. This offers a gravitational theory with a nonzero graviton mass. We calculate the complete set of background equations of motion. Also, we obtain the self-accelerating background solutions and we present the constraints on parameters to indicate the correct sign of parameters. In addition, we analyse tensor perturbations and calculate the mass of graviton and find the dispersion relation of gravitational waves for two cases. Finally, we investigate the propagation of gravitational perturbation in the Friedman-Lema\^{\i}tre-Robertson-Walker cosmology in the Gauss-Bonnet quasi-dilaton massive gravity.
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