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

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 ($P_{3D}$), which carries cosmological information in Fourier space. On large scales, the three-dimensional correlation function (${\xi }_{3D}$) has provided robust measurements of the baryon acoustic oscillation (BAO) scale at 150~Mpc. On smaller scales, the one-dimensional power spectrum, $P_{1D}(k_{\Vert })$, has been the primary tool for extracting information. At the same time, the cross-spectrum, $P_{\times }(\theta ,k_{\Vert })$, has been introduced to incorporate angular information without the complications caused by survey window functions. We propose an analytical forward-modeling framework to reconstruct $P_{3D}$ from all these observables, based on the mathematical relation between them and $P_{3D}$. 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 $P_{3D}$ 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 $P_{3D}$ estimation.

15 pages, 13 figures. Accepted to PRD

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