Gravitational Wave Polarization Modes in $f(R)$ Theories

TL;DR

This paper clarifies the polarization modes of gravitational waves in $f(R)$ theories, showing the existence of an overlooked transverse breathing mode and addressing previous inconsistencies in the literature.

Contribution

It demonstrates that the transverse breathing mode exists in $f(R)$ theories and clarifies the limitations of the Lorenz gauge in non-Minkowski backgrounds.

Findings

Identification of the transverse breathing mode in $f(R)$ theories

Clarification of gauge conditions in non-Minkowski backgrounds

Resolution of previous inconsistencies in polarization mode analysis

Abstract

Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in $f(R)$ theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show that this is in general not possible and, in particular, that the traceless condition cannot be imposed due to the fact that we no longer have a Minkowski background metric. Our findings are in agreement with the results found using the Newman-Penrose formalism, and thus clarify the inconsistencies found so far in the literature.