Correlation between opposite-helicity gravitons: Imprints on
  gravity-wave and microwave backgrounds
  We examine some of the roots of parity violation for gravitons and uncover a
closely related new effect: correlations between right and left handed
gravitons. Such correlators have spin 4 if they involve gravitons moving along
the same direction, and spin zero for gravitons moving with opposite
directions. In the first case, the most immediate implication would be a degree
of linear polarization for the tensor vacuum fluctuations, which could be seen
by gravity wave detectors sensitive enough to probe the primordial background,
its degree of polarization and anisotropies. Looking at the anisotropy of the
gravity waves linear polarization we identify the parity respecting and
violating components of the effect. The imprint on the CMB temperature and
polarization would be more elusive, since it averages to zero in the two-point
functions, appearing only in their cosmic variance or in fourth order
correlators. In contrast, spin zero correlations would have an effect on the
two point function of the CMB temperature and polarization, enhancing the $BB$
component if they were anti-correlations. Such correlations represent an
amplitude for the production of standing waves, as first envisaged by
Grishchuk, and could also leave an interesting signature for gravity wave
detectors.
