The Polarizations of Gravitational Waves

TL;DR

This paper investigates the polarization contents of alternative gravity theories like Horndeski and $f(R)$, revealing additional polarization modes beyond those predicted by General Relativity, with implications for gravitational wave detection.

Contribution

It analyzes the polarization modes in Horndeski and $f(R)$ gravity, identifying extra transverse and mixed polarizations, and discusses limitations of Newman-Penrose classification for massive modes.

Findings

Massless Horndeski predicts an extra transverse polarization.

Massive Horndeski and $f(R)$ have mixed longitudinal and breathing polarizations.

Pulsar timing arrays could detect these extra polarizations.

Abstract

The direct detection of gravitational waves by LIGO/Virgo opened the possibility to test General Relativity and its alternatives in the high speed, strong field regime. Alternative theories of gravity generally predict more polarizations than General Relativity, so it is important to study the polarization contents of theories of gravity to reveal the nature of gravity. In this talk, we analyzed the polarizations contents of Horndeski theory and $f(R)$ gravity. We found out that in addition to the familiar plus and cross polarizations, a \emph{massless} Horndeski theory predicts an extra transverse polarization, and there is a mix of the pure longitudinal and transverse breathing polarizations in the \emph{massive} Horndeski theory and $f(R)$ gravity. It is possible to use pulsar timing arrays to detect the extra polarizations in these theories. We also pointed out that the classification of polarizations using Newman-Penrose variables cannot be applied to the massive modes. It cannot be used to classify polarizations in Einstein-\ae ther theory or generalized TeVeS theory, either.