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 .