Gravitational-wave polarizations in generic linear massive gravity and generic higher-curvature gravity

We study the polarizations of gravitational waves (GWs) in two classes extended gravity theories. As a preparatory yet complete study, we formulate linear massive (MG) with generic mass terms non-Fierz--Pauli type by identifying all independent variables that obey Klein--Gordon-type equations. The dynamical degrees freedom (dofs) MG consist spin-2 and spin-0 modes, former breaking down into tensor (helicity-2), vector (helicity-1), one scalar (helicity-0) components, while latter just corresponding to scalar. find convenient ways decomposing modes each spin distinct combinations transverse longitudinal coefficients directly expressed parameters, thereby serving as useful tool measuring masses GWs. Then analyze perturbations higher-curvature (HCG) whose Lagrangian is an arbitrary polynomial Riemann tensor. When expanded around flat background, dofs this theory are identified massless spin-2, modes. its part encompasses identical structure MG, GWs HCG provide six on top ordinary In parallel representations for scalar-polarization connected parameters HCG. analysis HCG, employ methods; One takes full advantage partial equivalence between at level, whereas other relies upon gauge-invariant formalism. confirm results agree. also discuss methods determine GW-polarization measurements. It worth stressing our method determining does not require propagation speeds, whether absolute or relative, details waveforms