Inference of the optical depth to reionization $\tau$ from $\textit{Planck}$ CMB maps with convolutional neural networks

TL;DR

This paper introduces a neural network-based likelihood-free method to estimate the optical depth to reionization from Planck CMB maps, avoiding traditional power spectrum analysis and handling complex systematic effects.

Contribution

It presents the first neural network approach for direct inference of $ au$ from CMB maps, trained on realistic simulations including systematics, offering a novel, model-independent analysis method.

Findings

Neural network estimates of $ au$ are consistent with existing results.

The method achieves a larger uncertainty (~30%) compared to traditional techniques.

Demonstrates the potential of neural networks for future CMB data analysis.

Abstract

The optical depth to reionization, $\tau$, is the least constrained parameter of the cosmological $\Lambda$CDM model. To date, its most precise value is inferred from large-scale polarized CMB power spectra from the ${\it Planck}$ High-Frequency Instrument (HFI). These maps are known to contain significant contamination by residual non-Gaussian systematic effects, which are hard to model analytically. Therefore, robust constraints on $\tau$ are currently obtained through an empirical cross-spectrum likelihood built from simulations. In this paper, we present a likelihood-free inference of $\tau$ from polarized ${\it Planck}$ HFI maps which, for the first time, is fully based on neural networks (NNs). NNs have the advantage of not requiring an analytical description of the data and can be trained on state-of-the-art simulations, combining information from multiple channels. By using Gaussian sky simulations and ${\it Planck}$ ${\tt SRoll2}$ simulations, including CMB, noise, and residual instrumental systematic effects, we train, test and validate NN models considering different setups. We infer the value of $\tau$ directly from $Q$ and $U$ maps at $\sim 4^\circ$ pixel resolution, without computing power spectra. On ${\it Planck}$ data, we obtain $\tau_{NN}=0.058 \pm 0.008$, compatible with current EE cross-spectrum results but with a $\sim30\%$ larger uncertainty, which can be assigned to the inherent non-optimality of our estimator and to the retraining procedure applied to avoid biases. While this paper does not improve on current cosmological constraints, our analysis represents a first robust application of NN-based inference on real data and highlights its potential as a promising tool for complementary analysis of near-future CMB experiments, also in view of the ongoing challenge to achieve a detection of primordial gravitational waves.