A hierarchical field-level inference approach to reconstruction from sparse Lyman-$\alpha$ forest data

TL;DR

This paper presents a hierarchical, field-level Bayesian inference method using a semiclassical Lagrangian perturbation theory analogue to reconstruct 3D matter distribution from sparse Lyman-$\alpha$ forest data, improving speed and noise handling.

Contribution

It introduces a self-consistent hierarchical field-level model with a semiclassical LPT analogue, enhancing reconstruction accuracy and computational efficiency over traditional LPT-based models.

Findings

The method accelerates MCMC sampling via simulated annealing.

It improves noise properties compared to traditional LPT models.

Successful reconstruction of 3D matter distribution from mock sparse data.

Abstract

We address the problem of inferring the three-dimensional matter distribution from a sparse set of one-dimensional quasar absorption spectra of the Lyman-$\alpha$ forest. Using a Bayesian forward modelling approach, we focus on extending the dynamical model to a fully self-consistent hierarchical field-level prediction of redshift-space quasar absorption sightlines. Our field-level approach rests on a recently developed semiclassical analogue to Lagrangian perturbation theory (LPT), which improves over noise problems and interpolation requirements of LPT. It furthermore allows for a manifestly conservative mapping of the optical depth to redshift space. In addition, this new dynamical model naturally introduces a coarse-graining scale, which we exploited to accelerate the Markov chain Monte-Carlo (MCMC) sampler using simulated annealing. By gradually reducing the effective temperature of the forward model, we were able to allow it to first converge on large spatial scales before the sampler became sensitive to the increasingly larger space of smaller scales. We demonstrate the advantages, in terms of speed and noise properties, of this field-level approach over using LPT as a forward model, and, using mock data, we validated its performance to reconstruct three-dimensional primordial perturbations and matter distribution from sparse quasar sightlines.