Probing the f(R) formalism through gravitational wave polarizations

The direct observation of gravitational waves (GWs) in the near future, and the corresponding determination of the number of independent polarizations, is a powerful tool to test general relativity and alternative theories of gravity. In the present work we use the Newman-Penrose formalism to characterize GWs in quadratic gravity and in a particular class of f® Lagrangians. We find that both quadratic gravity and the f® theory belong to the most general invariant class of GWs, i.e., they can present up to six independent polarizations of GWs. For a particular combination of the parameters, we find that quadratic gravity can present up to five polarizations states. On the other hand, if we use the Palatini approach for f® theories, GWs present only the usual two transverse-traceless polarizations such as in general relativity. Thus, we conclude that the observation of GWs can strongly constrain the suitable formalism for these theories.