Imprints of gravitational-wave polarizations on projected tidal tensor in three dimensions

TL;DR

This paper explores how additional gravitational-wave polarizations influence galaxy shape distortions, proposing a method to detect these effects and test gravity theories using future galaxy surveys.

Contribution

It introduces a three-dimensional statistical framework to identify signatures of extra GW polarizations in galaxy shape correlations, including parity violation detection.

Findings

Extra polarization modes alter correlation function amplitudes and angular patterns.

Distinct propagation speeds of modes can reveal parity violation sources.

Framework enables testing of modified gravity theories with upcoming surveys.

Abstract

Gravitational waves (GWs) distort galaxy shapes through the tidal effect, offering a novel avenue to probe the nature of gravity. In this paper, we investigate how extra GW polarizations beyond those predicted by general relativity imprint observable signatures on galaxy shapes. Since galaxy shapes are measured as two-dimensional images projected onto the celestial sphere, we present three-dimensional statistical quantities of the projected tidal tensor sourced by the tensor perturbation. We show that the presence of extra polarization modes modifies both the amplitude and angular dependence of the correlation functions. Furthermore, we identify a distinct observational channel for probing parity violation in helicity-two and helicity-one modes. In particular, we show that if they propagate at different speeds, galaxy surveys can disentangle the source of parity violation. Our findings establish a theoretical framework for using upcoming large-scale galaxy surveys to test modified gravity theories through the polarization content of GWs.