Global analysis of tensor mode helicity

A detection of helicity in a primordial gravitational-wave background (GWB) would provide compelling evidence for parity violation in the early universe and point toward physics beyond the standard picture of inflation. Since big bang cosmology is not time translation invariant, we identify that the so-called ``regular'' and often-neglected ``irregular'' solutions are independent degrees of freedom that can in principle carry different, even opposite, helicities. We note that this possibility complicates the interpretation of a measured net helicity. To determine the sensitivity of various GW detector configurations to helicity, we introduce a universal helicity efficiency coefficient that provides a unified geometric description of helicity sensitivity across gravitational-wave detectors which generalizes and improves previous estimators. We apply this helicity efficiency coefficient to estimate the sensitivity of a range of future GW experiments to helicity across twenty orders of magnitude in frequency assuming a fully helical background with an amplitude just below the current constraints.