Two- and Three-Dimensional Probes of Parity in Primordial Gravity Waves
  We show that three-dimensional information is critical to discerning the
effects of parity violation in the primordial gravity-wave background. If
present, helical gravity waves induce parity-violating correlations in the
cosmic microwave background (CMB) between parity-odd polarization $B$-modes and
parity-even temperature anisotropies ($T$) or polarization $E$-modes.
Unfortunately, $EB$ correlations are much weaker than would be naively
expected, which we show is due to an approximate symmetry resulting from the
two-dimensional nature of the CMB. The detectability of parity-violating
correlations is exacerbated by the fact that the handedness of individual modes
cannot be discerned in the two-dimensional CMB, leading to a noise contribution
from scalar matter perturbations. In contrast, the tidal imprints of primordial
gravity waves fossilized into the large-scale structure of the Universe are a
three-dimensional probe of parity violation. Using such fossils the handedness
of gravity waves may be determined on a mode-by-mode basis, permitting future
surveys to probe helicity at the percent level if the amplitude of primordial
gravity waves is near current observational upper limits.
