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

We explore dark matter phenomenology in Myrzakulov $F(R,T)$ gravity, formulated via the vielbein approach in Weitzenböck 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 $\mathrm{\Lambda }$CDM, providing new insight into structure formation, gravitational lensing, and cosmic acceleration – all rooted in the geometry of spacetime.