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 parametrized test of GR using the parametrized 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 $\ell =|m|=2$ and dipole $\ell =|m|=1$ angular harmonics, with two frequency evolution models. For $\ell =|m|=2$, we find that within the extended PPE framework the scalar amplitude deviates from zero at the $2-3\sigma$ 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 $\mathrm{\Delta }\log \mathcal{Z}=4.67\pm 0.32$. The EM constraint on the polarization angle places very tight bounds on non-GR parameters; for instance, in the case $\ell =|m|=2$, 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.

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• Alternative gravity theories
• Astrophysical studies of gravity
• Experimental studies of gravity
• Gamma ray bursts
• General relativity
• Gravitation
• Gravitational waves
• Gravity in dimensions other than four