Gravitational Wave Polarizations in $f(R)$ Gravity and Scalar-Tensor Theory

TL;DR

This paper explores gravitational wave polarizations in $f(R)$ gravity and scalar-tensor theories, highlighting additional scalar modes and their potential detectability via pulsar timing arrays.

Contribution

It analyzes the polarization states predicted by $f(R)$ gravity and Horndeski theory, emphasizing the presence of scalar modes and their observational implications.

Findings

Presence of transverse breathing and longitudinal polarizations due to scalar modes.

Longitudinal polarization detection is challenging with interferometers.

Pulsar timing arrays may effectively detect longitudinal polarizations.

Abstract

The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in $f(R)$ gravity and Horndeski theory, both containing scalar modes. These theories predict that in addition to the familiar $+$ and $\times$ polarizations, there are transverse breathing and longitudinal polarizations excited by the massive scalar mode and the new polarization is a single mixed state. It would be very difficult to detect the longitudinal polarization by interferometers, while pulsar timing array may be the better tool to detect the longitudinal polarization.