Sensitivity of third-generation interferometers to extra polarizations in the Stochastic Gravitational Wave Background

TL;DR

This paper forecasts the sensitivity of third-generation gravitational wave interferometers to non-GR polarization modes in the stochastic background, highlighting potential detection limits and improvements over previous detectors.

Contribution

It provides a detailed analysis of the sensitivity of Einstein Telescope and Cosmic Explorer to all polarization modes, including scalar and vector, in the stochastic gravitational wave background.

Findings

Detection limits could reach $h_0^2\Omega^{T,V,S}_{GW} \approx 10^{-12}-10^{-11}$ after 5 years.

Network sensitivity to polarization modes can improve by a factor of 1000 compared to second-generation detectors.

Potential to distinguish scalar modes by analyzing detector angular responses at high frequencies.

Abstract

When modified theories of gravity are considered, at most six gravitational wave polarization modes are allowed and classified in tensor modes, the only ones predicted by General Relativity (GR), along with additional vector and scalar modes. Therefore, gravitational waves represent a powerful tool to test alternative theories of gravitation. In this paper, we forecast the sensitivity of third-generation ground-based interferometers, Einstein Telescope and Cosmic Explorer, to non-GR polarization modes focusing on the stochastic gravitational wave background. We consider the latest technical specifications of the two independent detectors and the full network in order to estimate both the optimal signal-to-noise ratio and the detectable energy density limits relative to all polarization modes in the stochastic background for several locations on Earth and orientations of the two observatories. By considering optimal detector configurations, we find that in 5 years of observation the detection limit for tensor and extra polarization modes could reach $h_0^2\Omega^{T,V,S}_{GW} \approx 10^{-12}-10^{-11}$, depending on the network configuration and the stochastic background (i.e., if only one among vector and scalar modes exists or both are present). This means that the network sensitivity to different polarization modes can be approximately improved by a factor $10^3$ with respect to second-generation interferometers. We finally discuss the possibility of breaking the scalar modes degeneracy by considering both detectors angular responses to sufficiently high gravitational wave frequencies.