We study the possibility of measuring the optical depth at reionization $\tau$ without relying on large-scale cosmic microwave background (CMB) polarization. Our analysis is driven by the need to obtain competitive measurements that can validate the state-of-the-art constraints on this parameter, widely based on $E$-mode polarization measurements at $\ell \le 30$. This need is partially motivated by the typical concerns regarding anomalies observed in the Planck large-scale CMB data as well as by the remarkable fact that, excluding these latter, $\tau$ consistently exhibits correlations with anomalous parameters, such as $A_{\mathrm{lens}}$ and ${\mathrm{\Omega }}_k$, suggesting that slightly higher values of the optical depth at reionization could significantly alleviate or even eliminate anomalies. Within the $\mathrm{\Lambda }$ cold dark matter model, our most constraining result is $\tau =0.080\pm 0.012$, obtained by combining Planck temperature and polarization data at $\ell >30$, the Atacama Cosmology Telescope (ACT) and Planck measurements of the lensing potential, baryon acoustic oscillations (BAOs), and type-Ia supernova data from the $\mathrm{Pantheon}+\text{catalog}$. Notably, using only ACT temperature, polarization, and lensing data in combination with BAOs and supernovae, we obtain $\tau =0.076\pm 0.015$, which is entirely independent of Planck. The relative precision of these results is approaching the constraints based on large-scale CMB polarization ($\tau =0.054\pm 0.008$). Despite the overall agreement, we report a slight $1.8\sigma$ shift toward larger values of $\tau$. We also test how these results change by extending the cosmological model. While in many extensions they remain robust, in general, obtaining precise measurements of $\tau$ may become significantly more challenging.

• Received 22 December 2023
• Accepted 18 April 2024

DOI:https://doi.org/10.1103/PhysRevD.109.103519

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society