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This study explores the cosmological implications of the $F(R, T)$quasi-dilaton massive gravity theory, a modification of the deRham-Gabadadze-Tolley (dRGT) massive gravity theory. Our analysis focuses onthe self-accelerating solution of the background equations of motion, which areshown to exist in the theory. Notably, we find that the theory features aneffective cosmological constant, which has important implications for ourunderstanding of the universe's accelerated expansion. To test the viability ofthe $F(R, T)$ quasi-dilaton massive gravity theory, we utilize the Union2 TypeIa Supernovae (SNIa) dataset, comprising 557 observations. Our resultsdemonstrate that the theory is capable of explaining the accelerated expansionof the universe without requiring the presence of dark energy. This findingsupports the potential of the $F(R, T)$ quasi-dilaton massive gravity theory asan alternative explanation for the observed cosmic acceleration. Moreover, weinvestigate the properties of tensor perturbations within the framework of thistheory and derive a novel expression for the dispersion relation ofgravitational waves. Our analysis reveals interesting features of the modifieddispersion relation in the Friedmann-Lema\^itre-Robertson-Walker cosmology,providing new insights into the nature of gravitational waves in the contest ofthe $F(R, T)$ quasi-dilaton massive gravity theory.

Cosmological Study in $F(R, T)$ Quasi-dilaton Massive Gravity