As massive gravity and its extensions offer physically well-defined gravitational theories with a nonzero graviton mass, we present a new extension of the de Rham–Gabadadze-Tolley massive gravity, which is a tachyonic massive gravity theory. We first introduce the new extension of the de Rham–Gabadadze-Tolley massive gravity, constructed by adding a tachyonic term. We then find the cosmological background equations, and present the analysis of self-accelerating solutions. We examine the tensor perturbations to calculate the dispersion relation of gravitational waves (GWs). In a special case, we consider a constant tachyon potential for the tachyon field $\sigma$, $V(\sigma )=2\omega /M_{\mathrm{Pl}}^2$, and calculate the equations of motion and the self-accelerating solutions. Finally, we investigate the background perturbations, which include tensor, vector, and scalar perturbations in this case. We calculate the dispersion relation of GWs in the Friedmann-Lemaître-Robertson-Walker cosmology in a tachyonic massive gravity theory. These analyses provide potential inputs to future applications in cosmology and GW propagations.

• Received 12 June 2021
• Accepted 9 December 2021

DOI:https://doi.org/10.1103/PhysRevD.105.023501