Bridging Simulations and EFT: A Hybrid Model of the Lyman-Alpha Forest Field

TL;DR

This work addresses the high-precision modeling needs of the Ly-α forest for DESI by introducing a hybrid forward model (HEFT) that couples non-linear particle displacements from AbacusSummit with a perturbative, Ly-α-specific EFT bias expansion in redshift space. By adverting bias operators with transfer functions and incorporating redshift-space distortions via Zel'dovich-based LOS displacements, HEFT achieves a nearly white stochastic residual and extends accurate modeling to $k\lesssim 1\,h\,\text{Mpc}^{-1}$, outperforming pure EFT. The results show 5% agreement with the true power spectrum and $r_{cc}>0.95$ up to $k$ around $1\,h\,\text{Mpc}^{-1}$ for realistic bias setups, enabling a potential doubling of effective modes and substantial reductions in cosmological parameter uncertainties. The framework lays the groundwork for fast Ly-α forest emulators and full-shape analyses, including cross-correlations with biased tracers, with broad applicability to DESI and future surveys.

Abstract

The Lyman-alpha (Lya) forest is a unique probe of cosmology and the intergalactic medium at high redshift and small scales. The statistical power of the ongoing Dark Energy Spectroscopic Instrument (DESI) demands precise theoretical tools to model the Lya forest. We present a hybrid effective field theory (HEFT) forward model in redshift space that leverages the accuracy of non-linear particle displacements computed using the N-body simulation suite AbacusSummit with the predictive power of an analytical, perturbative bias forward model in the framework of the effective field theory (EFT). The residual noise between the model and the simulated Lya field has a nearly white (scale-and orientation-independent) power spectrum on quasi-linear scales, substantially simplifying its modeling compared to a purely perturbative description. As a consequence of the improved control over the 3D Lya forest stochasticity, we find agreement between the modeled and the true power spectra at the 5 per cent level down to scales of k <= 1 h/Mpc. This procedure offers a promising path toward constructing efficient and accurate emulators to predict large-scale clustering summary statistics for full-shape cosmological analyses of Lya forest data from both DESI and its successor, DESI-II.

Figures (6)

• Figure 1: Error Power Spectrum: Comparison of the measured power spectrum on the AbacusSummit simulation (dash-dotted black line) for model one (left panel) and model three (right panel) to the error power spectra $P_{\mathrm{err}}(k,\mu) \equiv \langle |\delta^{\mathrm{truth}}_F - \delta^{\mathrm{model}}_F|^2 \rangle$ obtained from the EFT results (linear model as dotted black and cubic model as solid black line; deBelsunce:2025bqc) to the HEFT results (linear dashed blue, cubic solid red). In each panel, the power spectrum is shown in bins of Fourier wavenumber $k$ and angle to the line of sight, parametrized by $\mu = k_\parallel / k$, with decreasing line intensity for decreasing values of $\mu = 0.83,\, 0.50,\, 0.17$. The corresponding ratio plots of the power spectrum of the forward modeled field are given in Fig. \ref{['fig:Deltapk']} and the corresponding cross-correlation coefficients in Fig. \ref{['fig:rcc']}. Whilst linear theory shows a breakdown at all scales emphasizing the need for higher-order bias expansions to capture the non-linearities in the simulation, these results illustrate the scales at which HEFT yields the largest improvements ($k \hbox{$\; \buildrel > \over \sim \;$\xspace} 0.1 \,h\, {\rm Mpc}^{-1}\xspace$) by removing the scale and orientation dependence of the error power spectrum. The recovered error power spectra for the cubic HEFT model are approximately flat, following theoretical EFT predictions Ivanov:2023yla.
• Figure 2: Power Spectrum Residuals: Same as Fig. \ref{['fig:pk']} for the corresponding power spectrum residuals between the measured power spectrum from the AbacusSummit simulation ($P_{\mathrm{true}}$) and the power spectra of the forward modeled fields using HEFT with a linear (blue) and cubic (red) model compared to the forward model using an EFT model (linear as dotted black line, cubic as solid black line). We compare two models: one in the left panel and three in the right panel and include a 5% gray error band to guide the eye. The power spectrum of the forward model agrees at the 5% level up to ${k_\text{max}}\simeq 0.8\,h\, {\rm Mpc}^{-1}\xspace$ for HEFT, increasing the reach of the forward model compared to EFT by $\Delta k\approx 0.15 \,h\, {\rm Mpc}^{-1}\xspace$.
• Figure 3: Cross-Correlation Coefficient: Same as Fig. \ref{['fig:Deltapk']} for the corresponding cross-correlation factor $r_{cc}(\delta_F^{\rm truth},\delta^{\rm model}_F)=\langle \delta^{\rm model}_F({\bm k}) [\delta_F^{\rm truth}({\bm k})]^* \rangle/ \langle (|\delta_F^{\rm truth}({\bm k})|^2\rangle \langle |\delta_F^{\rm model}({\bm k})|^2\rangle)^{1/2}$ between the simulation and the forward modeled field for model one (left panel) and model three (right panel) illustrating a small and large $b_\eta$ bias parameter, respectively. Following baseline expectation, HEFT improves the reach of the cross-correlation coefficient for both models down to scales of $k\sim 1 \,h\, {\rm Mpc}^{-1}\xspace$.
• Figure 4: Noise Power Fits: We fit the polynomial given in Eq. \ref{['eq:Perr_tf']} to the error power spectrum for model one (three) with low (large) $b_\eta$ bias parameter value in the top (bottom) panel. In a low-$b_\eta$ Universe, the scale-dependence is completely removed (model one), whereas model three with a large $b_\eta$ parameter exhibits a residual scale-dependence on large scales and a strongly suppressed one on intermediate to small scales. The comparison of the fits to the measured error power spectra emphasizes the performance gains obtained by HEFT on scales beyond $k\hbox{$\; \buildrel > \over \sim \;$\xspace} 0.2 \,h\, {\rm Mpc}^{-1}\xspace$.
• Figure 5: Transfer Function Measurements: Best-fit transfer functions $\beta_i(k,\mu)$ for the cubic HEFT model obtained from fits to the AbacusSummit simulation for model one (top panel) and model three (bottom panel). The corresponding polynomial model for the transfer functions $\beta(k,\mu)$ is given in Eq. \ref{['eq:beta_tf']} which reduces to the Kaiser model in the low-$k$ limit. The large fluctuations in the first two $k$-bins stem from the small number of available modes. Weighting each bin by its number of $k$ modes down weights very noisy bins. The coefficients are tabulated in Tab. \ref{['tab:beta_parameters']}.