Constraining the Polarization Content of Gravitational Waves with Astrometry

TL;DR

This paper explores how astrometry, especially Gaia, can detect and distinguish different polarization states of gravitational waves by analyzing their unique correlation patterns in star positions, offering a new test of Einstein's gravity.

Contribution

It computes the full polarization-dependent astrometric correlation patterns and decomposes them into vector spherical harmonics, revealing signatures of alternative gravity theories.

Findings

Tensor and vector modes produce equal electric and magnetic correlations.

Scalar modes generate only electric-type correlations.

Longitudinal modes show enhanced correlations at small angles.

Abstract

Gravitational waves perturb the paths of photons, impacting both the time-of-flight and the arrival direction of light from stars. Pulsar timing arrays can detect gravitational waves by measuring the variations in the time of flight of radio pulses, while astrometry missions such as Gaia can detect gravitational waves from the time-varying changes in the apparent position of a field of stars. Just as gravitational waves impart a characteristic correlation pattern in the arrival times of pulses from pulsars at different sky locations, the deflection of starlight is similarly correlated across the sky. Here we compute the astrometric correlation patterns for the full range of polarization states found in alternative theories of gravity, and decompose the sky-averaged correlation patterns into vector spherical harmonics. We find that the tensor and vector polarization states produce equal power in the electric- and magnetic-type vector spherical harmonics, while the scalar modes produce only electric-type correlations. Any difference in the measured electric and magnetic-type correlations would represent a clear violation of Einstein gravity. The angular correlations functions for the vector and scalar longitudinal modes show the same enhanced response at small angular separations that is familiar from pulsar timing.