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

Abstract

This review provides a comprehensive overview of Myrzakulov gravity, emphasizing key developments and significant results that have shaped the theory’s current understanding. The paper explores the foundational principles of this modified gravity framework, delving into the intricate structure of field equations, the incorporation of non-metricity, and the role of torsion in determining gravitational interactions. The theory’s implications extend beyond traditional gravitational physics, offering new perspectives on cosmology, astrophysical phenomena, and the behavior of matter and energy in the presence of strong gravitational fields. A particular focus is placed on the formulation of field equations within Myrzakulov gravity and their relation to standard Einstein-Hilbert theory, highlighting how the introduction of additional geometric terms and scalar fields influences the dynamics of the universe. The role of non-metricity is examined in detail, revealing how it modifies the geodesic motion and curvature of spacetime, leading to distinct observable effects compared to General Relativity. We discuss the incorporation of the modified Einstein-Hilbert action, which allows for the accommodation of dark energy and dark matter in the context of cosmological expansion and structure formation. Additionally, the paper surveys the applications of Myrzakulov gravity to a variety of astrophysical scenarios, such as black holes, gravitational waves, and the cosmic acceleration observed in the late universe. These applications illustrate the potential of the theory to offer alternative explanations for phenomena typically attributed to dark matter and dark energy. The review also highlights important constraints derived from observational data, including cosmological measurements and tests of gravitational wave propagation, that help refine the model’s predictions and determine its compatibility with the current understanding of the universe. With a selective focus on the most impactful outcomes and experimental validations, this review aims to provide a concise yet thorough examination of Myrzakulov gravity, addressing both its theoretical underpinnings and observational constraints. By presenting the theory in the broader context of modified gravity approaches, we explore its potential to reshape fundamental physics and offer novel insights into the mysteries of the cosmos.