A Measurement of the Largest-Scale CMB E-mode Polarization with CLASS

Abstract

We present measurements of large-scale cosmic microwave background (CMB) E-mode polarization from the Cosmology Large Angular Scale Surveyor (CLASS) 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay polarization modulator, we achieved a polarization sensitivity of 78 µK arcmin, comparable to Planck at similar frequencies (100 and 143 GHz). The analysis demonstrates effective mitigation of systematic errors and addresses challenges to large-angular-scale power recovery posed by time-domain filtering in maximum-likelihood map-making. A novel implementation of the pixel-space transfer matrix is introduced, which enables efficient filtering simulations and bias correction in the power spectrum using the quadratic cross-spectrum estimator. Overall, we achieved an unbiased time-domain filtering correction to recover the largest angular scale polarization, with the only power deficit, arising from map-making non-linearity, being characterized as less than 3%. Through cross-correlation with Planck, we detected the cosmic reionization at 99.4% significance and measured the reionization optical depth τ = 0.053⁺⁰˙⁰¹⁸₋₀.₀₁₉, marking the first ground-based attempt at such a measurement. At intermediate angular scales (ℓ>30), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck's measurements.