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Extra polarization states of cosmological gravitational waves in alternative theories of gravity

In general, the cosmological metric perturbations are decomposed in accordance with the spatial symmetry, i.e., in terms of scalar, vector and tensor perturbations. In this context, gravitational waves (GWs) are usually associated with the tensor components, which are the transverse-traceless part of the metric perturbations. Although the same approach can be carried out for any theory of gravity, in some cases GWs can present up to six independent polarizations. The number of independent polarizations of the GWs in any theory of gravity can be evaluated by the number of the non-null Newman-Penrose quantities of the theory. They are just the components of the Riemann tensor which generate relative accelerations in a ring of test articles. In the present work we write down the perturbations in a general form, which is particularly suitable to analyze cosmological extra polarization states for a wide range of alternative theories of gravity. As an example of application, we consider a general scalar-tensor theory for which GW have four polarization states and the Visser's bimetric theory with massive gravitons, which belongs to the most general class, having six polarization states for GWs.

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