In this thesis the geometrical methods and symmetry principles in gravitation are explored motivating a new perspective into the spacetime paradigm. The effects of post-Riemann spacetime geometries with torsion are studied in applications to fundamental fermionic and bosonic fields, cosmology, astrophysics and gravitational waves. The physical implications and related phenomenological considerations of this study are addressed, and the fundamental ideas related to spacetime physics, motivated by geometrical methods and symmetry principles, are also discussed in the context of the possible routes towards a new spacetime paradigm in gravitation and unified field theories.
We explore the analogies between the gauge approach to gravity and the pre-metric approach to electrodynamics, within the exterior calculus of forms. These analogies are developed, reinforcing the hypothesis of the primacy of the conformal structure over the metric structure. Since the conformal symmetries seem to be broken symmetries in nature, the Poincar´e gauge theories of gravity (PGTG) are taken into consideration.
These presuppose a Riemann-Cartan (RC) spacetime geometry with curvature and torsion and motivate the search for torsion effects in physical systems. We study both minimal and non-minimal couplings of fermionic spinors to the background torsion and find changes in the energy levels (in the flat spacetime limit), including parity breaking effects. The Einstein-Cartan-Dirac-Maxwell theory is explored including its cosmological applications. The presence of minimal couplings to torsion induces non-linearities and non-minimal couplings in the matter fields dynamics and the resulting cosmological model is non-singular, including early and future bounces, early acceleration and torsion induced dark-energy due to fermionic vacuum condensates. Some potential astrophysical applications due to the torsion interaction with fermionic and bosonic fields are also considered as well as the effects of curvature in electromagnetic fields, including the extensions with inhomogeneous and anisotropic constitutive electromagnetic relations that respect the local isometries. In this context, the Parametrized Post-Newtonian (PPN) formalism is also implemented, making a bridge with the testing of different gravity theories. The effects of torsion are also analysed in gravitational wave (GW) physics, following the perturbations of a RC spacetime and in the field equations of a specific quadratic PGTG. The gravitational wave effects into electromagnetic fields are also studied with potential applications for non-standard detectors, which in principle could be extended for theories beyond GR, searches of extra polarizations and extra degrees of freedom
