Polarized Sunyaev Zel'dovich tomography
  Secondary CMB polarization is induced by the late-time scattering of CMB
photons by free electrons on our past light cone. This polarized Sunyaev
Zel'dovich (pSZ) effect is sensitive to the electrons' locally observed CMB
quadrupole, which is sourced primarily by long wavelength inhomogeneities. By
combining the remote quadrupoles measured by free electrons throughout the
Universe after reionization, the pSZ effect allows us to obtain additional
information about large scale modes beyond what can be learned from our own
last scattering surface. Here we determine the power of pSZ tomography, in
which the pSZ effect is cross-correlated with the density field binned at
several redshifts, to provide information about the long wavelength Universe.
The signal we explore here is a power asymmetry in the cross-correlation
between $E$ or $B$ mode CMB polarization and the density field. We compare this
to the cosmic variance limited noise: the random chance to get a power
asymmetry in the absence of a large scale quadrupole field. By computing the
necessary transfer functions and cross-correlations, we compute the
signal-to-noise ratio attainable by idealized next generation CMB experiments
and galaxy surveys. We find that a signal-to-noise ratio of $\sim 1-10$ is in
principle attainable over a significant range of power multipoles, with the
strongest signal coming from the first multipoles in the lowest redshift bins.
These results prompt further assessment of realistically measuring the pSZ
signal and the potential impact for constraining cosmology on large scales.
