Cross-spectra likelihood for robust $\tau$ constraints from all satellite polarisation data

TL;DR

This paper introduces 'elica', a new multi-frequency likelihood combining satellite CMB polarisation data to improve constraints on the optical depth to reionisation, with robust validation and implications for neutrino mass and cosmological tensions.

Contribution

The paper presents 'elica', a novel harmonic-space likelihood that combines multiple satellite datasets for more accurate and unbiased $ au$ estimation, validated with realistic simulations.

Findings

Measured $ au$ consistent with low values, confirming previous results.

Combining datasets reduces bias and maintains uncertainty levels.

Provides a publicly available likelihood for future analyses.

Abstract

The Thomson scattering optical depth to reionisation, $\tau$, one of the six parameters of the $\Lambda$CDM model, is primarily constrained by the large-scale E-mode polarisation of the Cosmic Microwave Background (CMB). In this work, we present the E-mode Likelihood for Cross-Analysis (elica), a multi-frequency, harmonic-space likelihood that combines all currently available large-scale satellite polarisation data, namely the Planck LFI 70 GHz channel, the Planck HFI 100 and 143 GHz channels processed with the SRoll2 map-making algorithm, and the WMAP Ka, Q, and V bands. The likelihood is built on an extension of the Hamimeche-Lewis formalism to multi-field partial-sky observations. We validate the pipeline using 500 realistic simulations and find that retaining all cross-spectra and the WMAP-LFI auto-spectrum eliminates the significant bias present when all spectra are retained, while preserving comparable uncertainties in the recovered value of $\tau$. From the low-$\ell$ E-mode power spectrum alone, we obtain $\tau = 0.0575_{-0.0058}^{+0.0048}$ (68% CL). Combining elica with the Planck low-$\ell$ temperature likelihood and the CamSpec high-$\ell$ likelihood, we find $\tau = 0.0581_{-0.0059}^{+0.0048}$ and $\ln(10^{10}A_{\mathrm{s}}) = 3.048_{-0.012}^{+0.011}$. Including ACT{} DR6 + Planck CMB lensing and DESI DR2 BAO measurements, we derive an upper bound on the total neutrino mass of $\sum m_\nu < 0.069$ eV (95% CL). Our results, obtained through careful cross-validation of all available large-scale polarisation datasets, robustly confirm that the optical depth remains relatively low. This severely constrains the possibility of explaining, or even significantly reducing, the tension between DESI-BAO and CMB observations with a high value of $\tau$. The elica likelihood is publicly available.