Testing for Lorentz Invariance Violation through Birefringence Effects of Gravitational Waves

General Relativity and the Standard Model are two experimentally supported theories, yet a consistent unified quantum theory of gravity at the Planck scale is still to be found. Built into these theories are CPT and Lorentz Symmetries; attempts to unify the two theories may involve breaking these symmetries. Using the effective theory framework, the Standard Model Extension (SME) lays out all possible background field tensors that can couple to known fields. In this way, one can test for the generic symmetric breaking of existing fields. In particular, we discuss using LIGO-VIRGO gravitational wave data as a means of testing Lorentz symmetry. A possible observable effect is birefringence, where there would be a small shift in the arrival times between the two gravitational wave polarizations from a distant source to detectors.