# Two- and Three-Dimensional Probes of Parity in Primordial Gravity Waves

## TL;DR

This paper emphasizes the importance of three-dimensional data in detecting parity violation in primordial gravity waves, highlighting the limitations of CMB measurements and proposing large-scale structure fossils as a more effective probe.

## Contribution

It demonstrates that three-dimensional large-scale structure fossils can effectively detect parity violation in primordial gravity waves, overcoming limitations of two-dimensional CMB observations.

## Key findings

- $EB$ correlations are weaker than expected due to symmetry.
- Two-dimensional CMB cannot determine the handedness of modes.
- Fossils in large-scale structure enable mode-by-mode parity analysis.

## Abstract

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.