Measuring the net circular polarization of the stochastic gravitational wave background with interferometers

TL;DR

This paper explores methods for detecting the net circular polarization of the stochastic gravitational wave background using interferometers, focusing on anisotropy induced by Earth's motion and analyzing the capabilities of LISA, ET, and ground-based networks.

Contribution

It introduces a new approach to measure circular polarization via dipolar anisotropy and provides detailed sensitivity estimates for LISA, ET, and detector networks.

Findings

LISA and ET can detect net circular polarization at SNR ~1 for h^2Ω_GW ≈ 10^{-11}

New analytical formulas for detector overlap functions with circular polarization

Planar detectors alone cannot measure isotropic SGWB polarization

Abstract

Parity violating interactions in the early Universe can source a stochastic gravitational wave background (SGWB) with a net circular polarization. In this paper, we study possible ways to search for circular polarization of the SGWB with interferometers. Planar detectors are unable to measure the net circular polarization of an isotropic SGWB. We discuss the possibility of using the dipolar anisotropy kinematically induced by the motion of the solar system with respect to the cosmic reference frame to measure the net circular polarization of the SGWB with planar detectors. We apply this approach to LISA, re-assessing previous analyses by means of a more detailed computation and using the most recent instrument specifications, and to the Einstein Telescope (ET), estimating for the first time its sensitivity to circular polarization. We find that both LISA and ET, despite operating at different frequencies, could detect net circular polarization with a signal-to-noise ratio of order one in a SGWB with amplitude $h^2 \Omega_\text{GW} \simeq 10^{-11}$. We also investigate the case of a network of ground based detectors. We present fully analytical, covariant formulas for the detector overlap functions in the presence of circular polarization. Our formulas do not rely on particular choices of reference frame, and can be applied to interferometers with arbitrary angles among their arms.