Sensitivity to a Frequency-Dependent Circular Polarization in an
  Isotropic Stochastic Gravitational Wave Background
  We calculate the sensitivity to a circular polarization of an isotropic
stochastic gravitational wave background (ISGWB) as a function of frequency for
ground- and space-based interferometers and observations of the cosmic
microwave background. The origin of a circularly polarized ISGWB may be due to
exotic primordial physics (i.e., parity violation in the early universe) and
may be strongly frequency dependent. We present calculations within a coherent
framework which clarifies the basic requirements for sensitivity to circular
polarization, in distinction from previous work which focused on each of these
techniques separately. We find that the addition of an interferometer with the
sensitivity of the Einstein Telescope in the southern hemisphere improves the
sensitivity of the ground-based network to circular polarization by about a
factor of two. The sensitivity curves presented in this paper make clear that
the wide range in frequencies of current and planned observations ($10^{-18}\
{\rm Hz} \lesssim f \lesssim 100\ {\rm Hz}$) will be critical to determining
the physics that underlies any positive detection of circular polarization in
the ISGWB. We also identify a desert in circular polarization sensitivity for
frequencies between $10^{-15}\ {\rm Hz} \lesssim f \lesssim 10^{-3}\ {\rm Hz}$,
given the inability for pulsar timing arrays and indirect-detection methods to
distinguish the gravitational wave polarization.
