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

This study explores the cosmological implications of the Myrzakulov $F(R, T)$ quasi-dilaton massive gravity theory, a modification of the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory. Our analysis focuses on the self-accelerating solution of the background equations of motion, which are shown to exist in the theory. Notably, we find that the theory features an effective cosmological constant corresponding to the massive graviton, which has important implications for our understanding of the universe's accelerated expansion. To assess the validity of the Myrzakulov $F(R, T)$ quasi-dilaton massive gravity theory, we employ two datasets: the Union2 Type Ia Supernovae (SNIa) dataset, consisting of 557 observations, and the Pantheon SNIa data, which includes 1048 SNe I-a events gathered from diverse SN I-a samples. Our results demonstrate that the theory is capable of explaining the accelerated expansion of the universe without requiring the presence of dark energy. This finding supports the potential of the Myrzakulov $F(R, T)$ quasi-dilaton massive gravity theory as an alternative explanation for the observed cosmic acceleration. Moreover, we investigate the properties of tensor perturbations within the framework of this theory and derive a novel expression for the dispersion relation of gravitational waves. Our analysis reveals interesting features of the modified dispersion relation in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology, providing new insights into the nature of gravitational waves in the context of the Myrzakulov $F(R, T)$ quasi-dilaton massive gravity theory.