  The detection and characterization of primordial gravitational waves through
their impact on the polarization anisotropies of the cosmic microwave
background (CMB) is a primary science goal of current and future observations
of the CMB. An ancillary dataset that will become accessible with the great
leaps in sensitivity of CMB experiments is the polarized Sunyaev Zel'dovich
(pSZ) effect, small-scale CMB polarization anisotropies induced by scattering
from free electrons in the post-reionization Universe. The cross correlation of
the pSZ effect with galaxy surveys, a technique known as pSZ tomography, can be
used to reconstruct the remote quadrupole field: the CMB quadrupole observed
from different locations in the Universe. Primordial gravitational waves leave
a distinct imprint on the remote quadrupole field, making pSZ tomography a
potential new method to characterize their properties. Building on previous
work, we explore the utility of the full set of correlations between the
primary CMB and the reconstructed remote quadrupole field to both provide
exclusion limits on the amplitude of primordial gravitational waves, as well as
to provide constraints on several phenomenological models of the tensor sector:
axion gauge field inflation, general models with chiral tensors, and models
with modified late-time decay of tensors. We find that relatively futuristic
experimental requirements are necessary to provide competitive exclusion limits
compared with the primary CMB. However, pSZ tomography can be a powerful probe
of the late-time evolution of tensors and, through cross-correlations with the
primary CMB, can provide mild improvements on parameter constraints in various
models with chiral primordial gravitational waves.
