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

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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.

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Authors and Affiliations

  1. Northeast Community College, 801 E Benjamin Ave, 68701, Norfolk, NE, USA

    Davood Momeni

  2. Centre for Space Research, North-West University, Potchefstroom, 2520, South Africa

    Davood Momeni

  3. Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana, 010009, Kazakhstan

    Ratbay Myrzakulov

  4. L. N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan

    Ratbay Myrzakulov

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  1. Davood Momeni
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  2. Ratbay Myrzakulov
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Contributions

Davood Momeni and Ratbay Myrzakulov contributed equally to the development and completion of this manuscript.

Davood Momeni was primarily responsible for the conceptualization of the research, the formulation of the theoretical models, and the initial drafting of the manuscript. He contributed significantly to the interpretation of the results and their implications in the context of gravity theories. Additionally, he was involved in the revision and refinement of the manuscript during the peer review process.

Ratbay Myrzakulov contributed to the development of the theoretical framework and mathematical modeling. He provided key insights and guidance on the applications of the metric-affine gravity theories, and assisted in the analysis of the models. Ratbay Myrzakulov also participated in the writing and revision of the manuscript, contributing to the clarity and depth of the presentation.

Both authors approved the final version of the manuscript and agree to be accountable for the work presented.

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Correspondence to Davood Momeni.

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Momeni, D., Myrzakulov, R. Metric-Affine Myrzakulov Gravity Theories: Models, Applications and Theoretical Developments. Int J Theor Phys 64, 95 (2025). https://doi.org/10.1007/s10773-025-05966-y

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