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Cosmological Gravitational Waves (GWs) are usually associated with thetransverse-traceless part of the metric perturbations in the context of thetheory of cosmological perturbations. These modes are just the usualpolarizations `+' and `x' which appear in the general relativity theory.However, in the majority of the alternative theories of gravity, GWs canpresent more than these two polarization states. In this context, theNewman-Penrose formalism is particularly suitable for evaluating the number ofnon-null GW modes. In the present work we intend to take into account theseextra polarization states for cosmological GWs in alternative theories ofgravity. As an application, we derive the dynamical equations for cosmologicalGWs for two specific theories, namely, a general scalar-tensor theory whichpresents four polarization states and a massive bimetric theory which is in themost general case with six polarization states for GWs. The mathematical toolpresented here is quite general, so it can be used to study cosmologicalperturbations in all metric theories of gravity.

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