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.
Bibliographical noteFunding Information:
We would like to thank Thomas Dent, Gregg Harry, Joe Romano, and Alan Weinstein for their careful reading of this manuscript, as well as many members of the LIGO-Virgo Collaboration Stochastic Backgrounds working group for helpful comments and conversation. T. C. and M. I. are members of the LIGO Laboratory, supported by funding from the U.S. National Science Foundation. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under Cooperative Agreement No. PHY-0757058. N. C. and J. T. are supported by NSF Grant No. PHY-1505373. The work of A. M. was supported in part by the NSF Grant No. PHY-1204944 at the University of Minnesota. M. S. is partially supported by STFC (UK) under the Research Grant No. ST/L000326/1. E. T. is supported through ARC FT150100281 and CE170100004. This paper carries the LIGO document number LIGO-P1700059 and King’s College London report number KCL-PH-TH/2017-25.