Metric-Affine Myrzakulov Gravity Theories: Models, Applications and Theoretical Developments

This review presents a comprehensive overview of Myrzakulov gravity, highlighting key developments and significant results shaping the theory. It examines the foundational principles, field equations, and the role of non-metricity and torsion in gravitational interactions. The theory's implications extend to cosmology, astrophysics, and strong gravitational fields, offering alternatives to dark matter and dark energy. A focus is placed on the modified Einstein-Hilbert action, its impact on cosmic expansion, and astrophysical applications such as black holes and gravitational waves. Observational constraints from cosmology and gravitational wave tests are discussed to refine the model. By situating Myrzakulov gravity within the broader context of modified gravity, this review explores its potential to reshape fundamental physics.