# Polarization-based Tests of Gravity with the Stochastic Gravitational-Wave Background

## TL;DR

This paper proposes a Bayesian method to detect and analyze gravitational-wave polarizations in the stochastic background, aiming to test general relativity and constrain alternative theories using current and future detectors.

## Contribution

It introduces a novel Bayesian approach for polarization analysis of the stochastic gravitational-wave background, enhancing parameter estimation with multiple detectors.

## Key findings

- Advanced Virgo improves parameter estimation for mixed polarizations.
- The method can set limits on vector and scalar polarizations.
- Detection prospects are limited with current detectors but can be improved with additional observatories.

## Abstract

The direct observation of gravitational waves with Advanced LIGO and Advanced Virgo offers novel opportunities to test general relativity in strong-field, highly dynamical regimes. One such opportunity is the measurement of gravitational-wave polarizations. While general relativity predicts only two tensor gravitational-wave polarizations, general metric theories of gravity allow for up to four additional vector and scalar modes. The detection of these alternative polarizations would represent a clear violation of general relativity. The LIGO-Virgo detection of the binary black hole merger GW170814 has recently offered the first direct constraints on the polarization of gravitational waves. The current generation of ground-based detectors, however, is limited in its ability to sensitively determine the polarization content of transient gravitational-wave signals. Observation of the stochastic gravitational-wave background, in contrast, offers a means of directly measuring generic gravitational-wave polarizations. The stochastic background, arising from the superposition of many individually unresolvable gravitational-wave signals, may be detectable by Advanced LIGO at design-sensitivity. In this paper, we present a Bayesian method with which to detect and characterize the polarization of the stochastic background. We explore prospects for estimating parameters of the background, and quantify the limits that Advanced LIGO can place on vector and scalar polarizations in the absence of a detection. Finally, we investigate how the introduction of new terrestrial detectors like Advanced Virgo aid in our ability to detect or constrain alternative polarizations in the stochastic background. We find that, although the addition of Advanced Virgo does not notably improve detection prospects, it may dramatically improve our ability to estimate the parameters of backgrounds of mixed polarization.