Dark Matter Constraints in Myrzakulov $F(R,T)$ Gravity: A Vielbein Approach in Weitzenb\"{o}ck Spacetime with Observational Data

TL;DR

This paper investigates a torsion-based modified gravity model in Weitzenb"ock spacetime, using observational data to show it can mimic dark matter effects and serve as an alternative to the standard cosmological model.

Contribution

It introduces a vielbein formulation of Myrzakulov $F(R,T)$ gravity in Weitzenb"ock spacetime and constrains it with observational data, demonstrating its potential to explain dark matter phenomena geometrically.

Findings

Model reproduces galaxy rotation curves without dark matter

Consistent with Planck CMB and weak lensing data

Offers an alternative explanation for cosmic acceleration

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.