Probing the f(R) formalism through gravitational wave polarizations

TL;DR

This paper investigates how different f(R) gravity models affect gravitational wave polarizations, showing that some models predict additional polarizations beyond general relativity, which can be tested with future GW observations.

Contribution

It characterizes GW polarizations in quadratic and f(R) gravity theories using Newman-Penrose formalism, revealing the potential for up to six polarizations and the impact of formalism choice.

Findings

Quadratic gravity can have up to five GW polarizations.

f(R) theories in Palatini formalism have only two polarizations.

GW observations can distinguish between gravity formalisms.

Abstract

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(R) Lagrangians. We find that both quadratic gravity and the f(R) 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(R) 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.