Gravitational waves in general relativity contain two polarization degrees of freedom, commonly labeled plus and cross. Besides those two tensor modes, generic theories of gravity predict up to four additional polarization modes: two scalar and two vector. Detection of nontensorial modes in gravitational wave data would constitute a clean signature of physics beyond general relativity. Previous measurements have pointed to the unambiguous presence of tensor modes in gravitational waves, but the presence of additional generic nontensorial modes has not been directly tested. We propose a model-independent analysis capable of detecting and characterizing mixed tensor and nontensor components in transient gravitational wave signals, including those from compact binary coalescences. This infrastructure can constrain the presence of scalar or vector polarization modes on top of the tensor modes predicted by general relativity. Our analysis is morphology-independent (as it does not rely on a waveform templates), phase-coherent, and agnostic about the source sky location. We apply our analysis to data from GW190521 and simulated data and demonstrate that it is capable of placing upper limits on the strength of nontensorial modes when none are present, or characterizing their morphology in the case of a positive detection. Tests of the polarization content of a transient gravitational wave signal hinge on an extended detector network, wherein each detector observes a different linear combination of polarization modes. We therefore anticipate that our analysis will yield precise polarization constraints in the coming years, as the current ground-based detectors LIGO Hanford, LIGO Livingston, and Virgo are joined by KAGRA and LIGO India.
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