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Gravitational waves (GWs) have opened a new window on fundamental physics ina number of important ways. The next generation of GW detectors may reveal moreinformation about the polarization structure of GWs. Additionally, there isgrowing interest in theories of gravity beyond GR. One such theory whichremains viable within the context of recent measurements of the speed ofpropagation of GWs is the teleparallel analogue of Horndeski gravity. In thiswork, we explore the polarization structure of this newly proposed formulationof Horndeski theory. In curvature-based gravity, Horndeski theory is almostsynonymous with extensions to GR since it spans a large portion of thesepossible extensions. We perform this calculation by taking perturbations abouta Minkowski background and consider which mode propagates. The result is thatthe polarization structure depends on the choice of model parameters in theteleparallel Horndeski Lagrangian with a maximum of seven propagating degreesof freedom. While the curvature-based Horndeski results follows as a particularlimit within this setup, we find a much richer structure of both massive andmassless cases which produce scalar--vector--tensor propagating degrees offreedom. We also find that the GW polarization that emerges from theteleparallel analogue of Horndeski gravity results in analogous massive andmassless modes which take on at most four polarizations in the massless sectorand two scalar ones in the massive sector. In none of the cases do we findvector polarizations.

Gravitational Wave Propagation and Polarizations in the Teleparallel analog of Horndeski Gravity