Measuring stochastic gravitational-wave energy beyond general relativity
Gravity theories beyond general relativity (GR) can change the properties of gravitational waves: their polarizations, dispersion, speed, and, importantly, energy content are all heavily theory dependent. All these corrections can potentially be probed by measuring the stochastic gravitational-wave background. However, most existing treatments of this background beyond GR overlook modifications to the energy carried by gravitational waves, or rely on GR assumptions that are invalid in other theories. This may lead to mistranslation between the observable cross-correlation of detector outputs and gravitational-wave energy density, and thus to errors when deriving observational constraints on theories. In this article, we lay out a generic formalism for stochastic gravitational-wave searches, applicable to a large family of theories beyond GR. We explicitly state the (often tacit) assumptions that go into these searches, evaluating their generic applicability, or lack thereof. Examples of problematic assumptions are as follows: statistical independence of linear polarization amplitudes; which polarizations satisfy equipartition; and which polarizations have well-defined phase velocities. We also show how to correctly infer the value of the stochastic energy density in the context of any given theory. We demonstrate with specific theories in which some of the traditional assumptions break down: Chern-Simons gravity, scalar-tensor theory, and Fierz-Pauli massive gravity. In each theory, we show how to properly include the beyond-GR corrections, and how to interpret observational results.
© 2018 American Physical Society. (Received 6 July 2018; published 16 November 2018) The authors would like to thank Laura Bernard, Tom Callister, Claudia de Rham, Kurt Hinterbichler, Andrew Matas, and Andrew Tolley for useful discussions. M. I. is an NHFP Einstein Fellow and is supported by NASA through the NASA Hubble Fellowship Grant No. HST–HF2–51410.001–A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under Contract No. NAS5–26555. M. I. is a member of the LIGO Laboratory. 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. L. C. S. acknowledges the support of NSF Grant No. PHY–1404569, and the Brinson Foundation. This paper carries LIGO Document No. LIGO-P1700234.
Published - PhysRevD.98.104025.pdf
Submitted - 1807.02123