Fermions and gravitational gyrotropy

Abstract

In conventional general relativity without torsion, high-frequency gravitational waves couple to the chiral number density of spin one-half quanta: the polarization of the waves is rotated by $2\pi N_5 {\ell_{\rm Pl}^2}$, where $N_5$ is the chiral column density and $\ell_{\rm Pl}$ is the Planck length. This means that if a primordial distribution of gravitational waves with E-E or B-B correlations passed through a chiral density of fermions in the very early Universe, an E-B correlation will be generated. This in turn will give rise to E-B and T-B correlations in the cosmic microwave background (CMB). Less obviously but more primitively, the condition Albrecht called "cosmic coherence" would be violated, changing the restrictions on the class of admissible cosmological gravitational waves. This altered class of waves would, generally speaking, probe earlier physics than do the conventional waves; their effects on the CMB would be most pronounced for low ($\lesssim 100$) multipoles. Rough estimates indicate that if the tensor-to-scalar ratio is less than about $10^{-2}$, it will be hard to constrain a spatially homogeneous primordial $N_5$ by present data.