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In general relativity, a gravitational wave has two polarization modes (tensor mode), but it could have additional polarizations (scalar and vector modes) in the early stage of the universe, where the general relativity may not strictly hold and/or the effect of higher-dimensional gravity may become significant.
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If a theory contains a parity-violating term, + + and × \times modes are polarized. Such a model predicts a GWB with circular polarizations. The detectability has been discussed in Seto and Taruya 2008 ; Seto 2007 ; Seto 2006 ; Seto and Taruya 2007
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