Implicit Likelihood Inference of the Neutrino Mass Hierarchy from Cosmological Data

TL;DR

This paper introduces a novel implicit likelihood inference pipeline using neural networks to analyze cosmological data for determining the neutrino mass hierarchy, achieving results consistent with the normal hierarchy.

Contribution

It develops a multi-round neural likelihood inference method embedding the CMB simulator into the pipeline, providing a new approach to cosmological parameter estimation.

Findings

Results slightly favor the normal neutrino mass hierarchy.

The method effectively estimates the neutrino hierarchy parameter from cosmological data.

Demonstrates the viability of neural implicit likelihood inference in cosmology.

Abstract

In this paper, we turn to the Learning the Universe Implicit Likelihood Inference (LtU-ILI) pipeline to perform a multi-round ILI of the neutrino mass hierarchy from cosmological data, including $TT$, $TE$, $EE$ power spectra of Planck 2018 and distance ratios of DESI DR2. More precisely, we first embed the CMB power spectra simulator $\mathtt{CLASS}$ into the LtU-ILI pipeline. And then, opting for Sequential Neural Likelihood Estimation (SNLE), we sequentially train neural networks using $2$ rounds of $5000$ simulations to target a ``black box'' likelihood of our forward model with one additional neutrino mass hierarchy parameter $\tilde{\Delta}$ and six base cosmological parameters. We find that $\tilde{\Delta}=0.12216^{+0.26193}_{-0.29243}~(68\%{\rm CL})$ which slightly prefers $\tilde{\Delta}>0$, hence the normal hierarchy.