Tests of General Relativity through Searches for Lorentz and CPT Symmetry Breaking

An effective field theory framework, the Standard Model Extension (SME), provides an agnostic, systematic test of General Relativity (GR) and its founding spacetime symmetries, Lorentz and CPT symmetry. Violating these symmetries may provide clues toward unifying the physics of the General Relativity and the Standard Model of particle physics. Part of this work involves the merge of theory, data analysis and experiments with gravitational wave (GW) signals from LIGO/Virgo/KAGRA (LVK) detectors. A modified dispersion relation derived from the SME of GWs is implemented into the LIGO Scientific Collaboration Algorithm Library Suite (LALSuite), where a joint Bayesian inference of the source parameters and coefficients for spacetime symmetry-breaking is performed for binary black hole and neutron star events. Using 45 events from the GWTC-3 LVK catalogue, constraints are placed on the symmetry-breaking coefficients. Additional work involves a 3+1 formulation of the SME in the gravitational sector with a Dirac Hamiltonian analysis. The assumption of explicit local Lorentz and diffeomorphism symmetry breaking is made. This work shows significant differences in the structure of the dynamics when comparing to General Relativity and focus is given to cosmological solutions, which produce modified Friedmann equations and altered conservation laws. This research also find terms within the framework to match certain modified gravity models along with noting further potential impact toward other gravitational models, theories and phenomenology including quantum gravity