Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity: Prospects for Unified Field Theories

Abstract

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.

33 pages. Invite review to the Special Issue "80 Years of Professor Wigner's Seminal Work "On Unitary Representations of the Inhomogeneous Lorentz Group"". Matches published version

References in corpus (14)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The Confrontation between General Relativity and Experiment
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• The teleparallel equivalent of general relativity
• Testing General Relativity with stellar orbits around the supermassive black hole in our Galactic center
• New classes of modified teleparallel gravity models
• Dark spinors with torsion in cosmology
• Wormholes and black universes without phantom fields in Einstein-Cartan theory
• Crystal clear lessons on the microstructure of space-time and modified gravity
• Probing non-Riemannian spacetime geometry
• Einstein-Cartan Gravity with Torsion Field Serving as Origin for Cosmological Constant or Dark Energy Density
• Gravitation, electromagnetism and cosmological constant in purely affine gravity
• Non-geodesic incompleteness in Poincaré gauge gravity