Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gauge theories of gravity, their field equations and Noether conserved currents, which are the sources of gravity. We then discuss several topics of the gauge approach to gravitational phenomena, namely, quadratic Poincaré gauge models, the Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of general relativity, quadratic metric-affine Lagrangians, non-Lorentzian connections, and the breaking of Lorentz invariance in the presence of non-metricity. We also highlight the probing of post-Riemannian geometries with test matter. Finally, we briefly discuss some perspectives regarding the role of both geometrical methods and symmetry principles towards unified field theories and a new spacetime paradigm, motivated from the gauge approach to gravity.

中文翻译：

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重力规理论中的基本对称性和时空几何-统一场论的前景

通过将对称原理和几何方法结合在一个一致的数学框架中，可以将重力公式化为规范理论。重力的量规方法直接导致了非欧几里德，后黎曼时空几何形状，为具有曲率，扭转和非度量性的公制仿射重力理论提供了充分的形式主义。在本文中，我们分析了重力规范理论的结构，并考虑了基本几何对象与对称性原理以及不同的时空范式之间的关系。特别注意庞加莱规范的引力理论，它们的场方程和Noether守恒电流，这是引力的来源。然后，我们讨论有关重力现象的轨距方法的几个主题，即二次庞加莱轨距模型，Einstein-Cartan-Sciama-Kibble理论，广义相对论的远平行等效，二次度量仿射拉格朗日算子，非洛伦兹联系以及在存在非度量性的情况下打破洛伦兹不变性。我们还将重点介绍用测试物质探测后黎曼几何。最后，我们简要讨论了关于几何方法和对称原理对统一场论和新的时空范式的作用的一些观点，这是由规范方法引力引起的。