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: 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.
