# Measuring the Homogeneity of the Universe Using Polarization Drift

## TL;DR

This paper introduces a novel method to test the universe's homogeneity by comparing expansion rates along different directions using polarization drift of CMB photons scattered by galaxy clusters, without assuming symmetry.

## Contribution

It presents a new observational approach to directly test the universe's isotropy at remote locations, crucial for validating the cosmological principle.

## Key findings

- Provides explicit formulas linking observables to metric properties.
- Demonstrates how polarization drift can probe transverse expansion.
- Suggests combining polarization data with baryon acoustic oscillations.

## Abstract

We propose a method to probe the homogeneity of a general universe, without assuming symmetry. We show that isotropy can be tested at remote locations on the past lightcone by comparing the line-of-sight and transverse expansion rates, using the time dependence of the polarization of Cosmic Microwave Background photons that have been inverse-Compton scattered by the hot gas in massive clusters of galaxies. This probes a combination of remote transverse and parallel components of the expansion rate of the metric, and we may use radial baryon acoustic oscillations or cosmic clocks to measure the parallel expansion rate. Thus we can test remote isotropy, which is a key requirement of a homogeneous universe. We provide explicit formulas that connect observables and properties of the metric.