  Cubic Galileon massive gravity is a development of de Rham-Gabadadze-Tolly
(dRGT) massive gravity theory is which the space of the Stueckelberg field is
broken. We consider the cubic Galileon term as a scalar field coupled to the
graviton filed. We present a detailed study of the cosmological aspects of this
theory of gravity. We analyze self-accelerating solutions of the background
equations of motion to explain the accelerated expansion of the Universe.
Exploiting the latest Union2 Type Ia Supernovea (SNIa) dataset, which consists
of 557 SNIa, we show that cubic Galileon massive gravity theory is consistent
with the observations. We also examine the tensor perturbations within the
framework of this model and find an expression for the dispersion relation of
gravitational waves, and show that it is consistent with the observational
results.
