Unified reconstruction of the Lyman-alpha power spectrum with Hamiltonian Monte Carlo

TL;DR

This paper introduces a unified analytical framework using Hamiltonian Monte Carlo to reconstruct the three-dimensional Lyman-alpha power spectrum from various two-point statistics, enabling more precise cosmological measurements.

Contribution

The paper presents a novel forward-modeling approach that combines multiple Lyman-alpha forest observables to accurately reconstruct the 3D power spectrum, improving consistency checks for future surveys.

Findings

Reconstructed $P_{3D}$ monopole in 25 $k$ bins with 13% average precision.

Demonstrated method's effectiveness using mock DESI-like data.

Provides a tool for consistency checks without replacing direct $P_{3D}$ estimation.

Abstract

The complex geometry of the Ly$\alpha$ forest data has motivated the use of various two-point statistics as alternatives to the three-dimensional power spectrum ($P_{\mathrm{3D}}$), which carries cosmological information in Fourier space. On large scales, the three-dimensional correlation function ($\xi_\mathrm{3D}$) has provided robust measurements of the baryon acoustic oscillation (BAO) scale at 150~Mpc. On smaller scales, the one-dimensional power spectrum, $P_{\mathrm{1D}}(k_\|)$, has been the primary tool for extracting information. At the same time, the cross-spectrum, $P_\times(\theta, k_\|)$, has been introduced to incorporate angular information without the complications caused by survey window functions. We propose an analytical forward-modeling framework to reconstruct $P_{\mathrm{3D}}$ from all these observables, based on the mathematical relation between them and $P_{\mathrm{3D}}$. We demonstrate the performance of our method using a hypothetical mock data vector representative of future Dark Energy Spectroscopic Instrument (DESI) measurements. We show that the monopole of $P_{\mathrm{3D}}$ can be reconstructed in 25 $k$ bins between $0.07~\mathrm{Mpc}^{-1}$ and $1.8~\mathrm{Mpc}^{-1}$, achieving an average precision of $\sigma_P/P=13\%$ across the bins. Our method can serve as an intermediary for consistency checks, though it is not intended to replace direct $P_{\mathrm{3D}}$ estimation.