Abstract
We introduce the Brans--Dick--de Rham--Gabadadze--Tolley massive gravity theory which is the new extension of nonlinear massive gravity. We demonstrate a detailed study of the cosmological properties of this theory of gravity, and we show the transformation of the Jordan frame to the Einstein frame. We obtain the cosmological background equations and show the analyses of self-accelerating solutions for explaining the accelerated expansion of the Universe. In the following, we analyze the background perturbations, which consist of tensor, vector, and scalar perturbations within the framework of the new extension of the de Rham--Gabadadze--Tolley massive gravity in the Friedman-Lema\^{\i}tre-Robertson-Walker cosmology.
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