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) Hz less than or similar to f less than or similar to 100 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) Hz less than or similar to f less than or similar to 10(-3) Hz, given the inability for pulsar timing arrays and indirect-detection methods to distinguish the gravitational wave polarization.