Polarization modes of gravitational waves in quadratic gravity

The observation of the inspiral and merger of compact binaries by the LIGO-Virgo collaboration has allowed for new tests of Einstein's theory in the extreme gravity regime, where gravitational interactions are simultaneously strong, non-linear, and dynamical. Theories beyond Einstein's can also be constrained by detecting the polarization modes of gravitational waves. In this talk, I will show that dynamical Chern-Simons gravity and Einstein-dilaton-Gauss-Bonnet gravity cannot be differentiated from general relativity based on the detection of polarization modes alone. To prove this result, I will be using the Newman-Penrose method and an irreducible decomposition method to find that only the tensorial (plus- and cross-polarization) modes can be detected in both these theories.