# Polarized Sunyaev Zel'dovich tomography

## TL;DR

This paper explores the potential of polarized Sunyaev Zel'dovich (pSZ) tomography to probe large-scale cosmological modes by cross-correlating CMB polarization with galaxy density fields across redshifts, highlighting its promise for future cosmological constraints.

## Contribution

It demonstrates the theoretical power of pSZ tomography to detect large-scale modes through polarization-density cross-correlations and estimates the signal-to-noise ratio for upcoming experiments.

## Key findings

- Signal-to-noise ratio of 1-10 for pSZ detection in idealized experiments.
- Strongest signals from low multipoles at low redshifts.
- Potential to improve understanding of large-scale cosmological modes.

## Abstract

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.