Unified reconstruction of the Lyman-alpha power spectrum with Hamiltonian Monte Carlo
N. G. Karac{c}ayl{i}, P. L. Taylor
arXiv:2506.08198v1 Announce Type: new
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 in a nearly model-independent way. We demonstrate the performance of our method using a hypothetical mock data vector representative of future Dark Energy Spectroscopic Instrument (DESI) measurements and 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 a median precision of $8%$ and a mean precision of $13%$. Our method can serve as an intermediary for consistency checks, though it is not intended to replace direct $P_{mathrm{3D}}$ estimation.arXiv:2506.08198v1 Announce Type: new
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 in a nearly model-independent way. We demonstrate the performance of our method using a hypothetical mock data vector representative of future Dark Energy Spectroscopic Instrument (DESI) measurements and 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 a median precision of $8%$ and a mean precision of $13%$. Our method can serve as an intermediary for consistency checks, though it is not intended to replace direct $P_{mathrm{3D}}$ estimation.