Dark Matter Constraints in Myrzakulov $F(R,T)$ Gravity: A Vielbein Approach in Weitzenböck Spacetime with Observational Data

Abstract: We explore dark matter phenomenology in Myrzakulov $F(R,T)$ gravity, formulated via the vielbein approach in Weitzenb\"{o}ck spacetime. In this torsion-based extension of gravity, dark matter emerges as a geometric effect rather than a particle species, with curvature and torsion contributing dynamically to the field equations. Using recent data -- including SPARC galaxy rotation curves, Planck CMB observations, and weak lensing from DES and KiDS -- we constrain the model through MCMC analysis. Our results show that, under specific parameter choices, the theory replicates key cosmological features without introducing additional dark sector matter. This framework offers a testable alternative to $\Lambda$CDM, providing new insight into structure formation, gravitational lensing, and cosmic acceleration -- all rooted in the geometry of spacetime.