Tests of scalar polarizations with multi-messenger events

Abstract

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 $\ell = |m|= 2$ 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 $2$--$3σ$ 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 $Δ\log \mathcal{Z} = 4.67 \pm 0.32$. 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.