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