Parity-violating defect sources and independent tensor-mode helicities

Investigate the implications of parity-violating topological-defect sources for the relative helicity content of regular and irregular tensor modes in a cosmological setting, thereby determining whether such sources can realize independent helicity structures.

Background

Regular and irregular tensor perturbation modes are independent solutions of the cosmological tensor perturbation equation and can, in principle, carry distinct helicities. Late-time sources such as topological defects may generate both modes without the divergent behavior associated with irregular modes produced at early times. Consequently, a source could produce regular and irregular modes with equal amplitudes but opposite helicities, causing the net helicity of the total gravitational-wave background to vanish even when each mode is individually helical.

The paper notes that existing discussions of topological-defect gravitational-wave production assume parity symmetry of the stress-energy tensor. The cosmological consequences of relaxing that assumption—specifically, how parity-violating defect sources determine the relative helicities of regular and irregular tensor modes—remain unstudied and could provide a concrete realization of the independent helicity structure proposed in the paper.