Cosmological Reconstructions in Einstein--Cartan--Myrzakulov Gravity with Torsion and Non-Metricity in the Weitzenböck Geometrical Sector

Abstract: The universe is a vast and complex system, and our understanding of its fundamental workings is constantly evolving. In this work, we present a novel modification to the standard theory of gravity by incorporating curvature, torsion, non-metricity, and the geometric structure of Weitzenb\"{o}ck spacetime. This modified framework, referred to as the Einstein--Cartan--Myrzakulov (ECM) model, enriched by Weitzenb\"{o}ck geometry, offers new insights into cosmological phenomena, including the accelerated expansion of the universe, the nature of dark energy and dark matter, and the formation of cosmic structures. Our model not only reproduces observed cosmic histories but also provides testable predictions that can be compared with current and future observational data. By addressing some of the most profound questions in modern cosmology, this work paves the way for a deeper understanding of the universe's evolution and the fundamental forces that govern it. The ECM model, extended through Weitzenb\"{o}ck spacetime, invites further exploration, offering the potential to revolutionize our conception of gravity and the cosmos.