Fermions and gravitational gyrotropy
  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.
