Tests of scalar polarizations with multi-messenger events

Gravitational wave (GW) observations provide a unique opportunity to test Einstein's General Relativity (GR) in the strong-field regime. While GR predicts only two tensor polarization modes, generic metric theories allow up to six independent modes. We perform a parameterized test of GR using the parameterized post-Einsteinian (PPE) framework applied to GW170817, incorporating for the first time the polarization angle constraints from the gamma-ray burst afterglow alongside other electromagnetic (EM) counterpart information. We extend the GR waveform by adding a scalar breathing mode and modifications to the tensor modes, introducing three non-GR parameters. We perform Bayesian inference for both quadrupole = m= 2 and dipole = m= 1 angular harmonics, with two frequency evolution models. For = m = 2, we find that within the extended PPE framework the scalar amplitude deviates from zero at the 2 -- 3σ level, leading to a modest preference for modified gravity. However, due to penalization of extra parameters, Bayesian model comparison still favors pure GR over the extended PPE waveform model, with a log Bayes factor of Δ Z = 4.67 plus or minus 0.32. The EM constraint on the polarization angle places very tight bounds on non-GR parameters; for instance, in the case = m = 2, the bound on the scalar (tensor) amplitude modification parameter improves by roughly 60% (30%), highlighting the impact that long-term follow up of GW events can have on tests of gravity.