Extracting parity-violating gravitational waves from projected tidal force tensor in three dimensions

TL;DR

This paper introduces a new method to detect parity-violating gravitational waves by analyzing the projected tidal force tensor in galaxy surveys, focusing on the curl-divergence properties to isolate GW signals.

Contribution

It develops a novel technique using the curl and divergence of the projected tidal field to extract parity-violating GW signals from galaxy survey data, complementing existing power spectrum methods.

Findings

The curl-divergence of the tidal field isolates GW signals free from scalar contamination.

Nonzero cross-correlation between divergence and curl indicates parity violation in GWs.

Derived Fourier integral expressions for correlation functions specific to GW detection.

Abstract

Gravitational waves (GWs) may be produced by various mechanisms in the early universe. In particular, if parity is violated, it may lead to the production of parity-violating GWs. In this paper, we focus on GWs on the scale of the large-scale structure. Since GWs induce tidal deformations of the shape of galaxies, one can extract such GW signals by observing images of galaxies in galaxy surveys. Conventionally the detection of such signals is discussed by considering the three-dimensional power spectra of the $E/B$-modes. Here, we develop a complementary new technique to estimate the contribution of GWs to the tidal force tensor field projected on the celestial sphere, which is a directly observable quantity. We introduce two two-dimensional vector fields constructed by taking the divergence and curl of the projected tidal field in three dimensions. Their auto-correlation functions naturally contain contributions of the scalar-type tidal field. However, we find that the divergence of the curl of the projected tidal field, which is a pseudo-scalar quantity, is free from the scalar contribution and thus enables us to extract GW signals. We also find that we can detect parity-violating signals in the GWs by observing the nonzero cross-correlation between the divergence of the projected tidal field and the curl of it. It roughly corresponds to measuring the cross-power spectrum of E and B-modes, but these are complementary to each other in the sense that our estimator can be naturally defined locally in position space. Finally we present expressions of the correlation functions in the form of Fourier integrals, and discuss the properties of the kernels specific to the GW case, which we call the overlap reduction function, borrowing the terminology used in the pulsar timing array experiments.