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 $78\,\mathrm{\mu K\,arcmin}$, 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 $\tau=0.053^{+0.018}_{-0.019}$, marking the first ground-based attempt at such a measurement. At intermediate angular scales ($\ell>30$), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck's measurements.

• The paper presents a novel measurement of large-scale CMB E-mode polarization using CLASS’s variable-delay modulator to achieve 78 μK arcmin sensitivity.
• It introduces a pixel-space transfer matrix that corrects map-making non-linearity with less than 3% power deficit for unbiased power spectrum recovery.
• The research cross-correlates CLASS and Planck data to obtain a reionization optical depth of τ = 0.053 at 99.4% significance, validating ground-based techniques.

Analysis of the Largest-Scale CMB E-Mode Polarization with CLASS

The paper presents a nuanced investigation into the largest angular scale polarization of the cosmic microwave background (CMB), conducted using data from the Cosmology Large Angular Scale Surveyor (CLASS) operating at 90 GHz. This research, spanning from 2021 to 2024, leverages the innovative capabilities of CLASS, notably its variable-delay polarization modulator, to achieve a polarization sensitivity of 78 $\mu K\,\mathrm{arcmin}$. This level of sensitivity is comparable to that of the Planck mission at similar frequencies, marking a significant contribution to ground-based CMB observations.

Methodological Advances

A key technical challenge addressed in this study was the mitigation of systematic errors inherent to large-angular-scale measurements. A novel pixel-space transfer matrix was developed, enabling efficient simulations and bias correction in the power spectrum analysis through the quadratic cross-spectrum estimator. This advancement allows for unbiased time-domain filtering corrections, essential for recovering large-angular-scale polarization signals. Notably, this implementation achieves a correction with power deficits due to map-making non-linearity characterized at under 3%.

The study also underscores the significance of cross-correlation with Planck data, which led to the detection of cosmic reionization at 99.4% significance. A pivotal outcome of the CLASS observations is the measurement of the reionization optical depth, $\tau = 0.053 ^{+0.018}_{-0.019}$. This represents the first attempt by a ground-based telescope to directly measure this parameter, aligning closely with the Planck results.

Validation and Implications

Extensive internal validation tests, including null tests and comparisons with Planck observations, confirm the reliability of the CLASS data. The null tests underscore the robustness of the data set, with only one notable inconsistency attributed to potential inadequacies in noise modeling under specific instrument configurations. The cross-correlation results not only corroborate the Planck findings but also serve to further validate the CLASS observational techniques.

The implications of this research are manifold. On a theoretical level, the measurement of large-scale E-mode polarization provides crucial insights into the epoch of reionization and enhances the detectability of inflationary gravitational waves through B-mode polarization. Practically, the study sets a precedent for future ground-based CMB experiments, demonstrating that they can indeed achieve the precision necessary to measure key cosmological parameters previously accessible only via space-based observatories.

Future Prospects

Building on this groundwork, further developments within CLASS, such as less aggressive filtering strategies and enhanced polarization modulation techniques, promise to significantly increase the precision of optical depth measurements, potentially reaching the cosmic variance limit. Additionally, the advent of a second 90 GHz telescope in 2025 will further enhance the sensitivity and sky coverage, unlocking new possibilities for detailed cosmological surveys.

In conclusion, the CLASS experiment at 90 GHz has marked a milestone in ground-based observational cosmology by effectively measuring the CMB polarization at the largest angular scales and providing a robust cross-verification of space-based measurements like those from Planck. This work not only substantiates the effectiveness of ground-based observations in probing the early universe but also points to a future where these methods will play an increasingly central role in cosmological discovery.