# Polarizations of Gravitational Waves in Horndeski Theory

## TL;DR

This paper investigates the polarization modes of gravitational waves in Horndeski theory, revealing an extra polarization due to a massive scalar field, which could be detected by pulsar timing arrays, offering insights into gravity's nature.

## Contribution

It identifies and characterizes the additional polarization states in Horndeski theory and discusses their potential detectability, advancing understanding of alternative gravity theories.

## Key findings

- Extra polarization mode exists beyond GR's plus and cross.
- Massive scalar field excites a mixture of breathing and longitudinal polarizations.
- Detection likelihood is limited by graviton mass constraints, but pulsar timing arrays may observe the breathing mode.

## Abstract

We analyze the polarization content of gravitational waves in Horndeski theory. Besides the familiar plus and cross polarizations in Einstein's General Relativity, there is one more polarization state which is the mixture of the transverse breathing and longitudinal polarizations.The additional mode is excited by the massive scalar field. In the massless limit, the longitudinal polarization disappears, while the breathing one persists. The upper bound on the graviton mass severely constrains the amplitude of the longitudinal polarization, which makes its detection highly unlikely by the ground-based or space-borne interferometers in the near future. However, pulsar timing arrays might be able to detect the polarization excited by the massive scalar field. Since additional polarization states appear in alternative theories of gravity, the measurement of the polarizations of gravitational waves can be used to probe the nature of gravity. In addition to the plus and cross states, the detection of the breathing polarization means that gravitation is mediated by massless spin 2 and spin 0 fields, and the detection of both the breathing and longitudinal states means that gravitation is propagated by the massless spin 2 and massive spin 0 fields.