Simulation-based inference from the Lyman-alpha forest 1D power spectrum with CAMELS

Abstract

We perform for the first time full simulation-based inference on the Lyman-$α$ forest 1D power spectrum. In particular, we consider the prediction of the Lyman-$α$ forest $P_{\rm 1D}(k)$ at $2.0<z<3.5$ from the CAMELS cosmological hydrodynamic simulations run with the IllustrisTNG and SIMBA galaxy formation models. We train a normalizing flow to perform neural posterior estimation of two cosmological parameters ($Ω_m$ and $σ_8$) and four astrophysical parameters parametrizing supernova and AGN feedback. When training and testing the neural network on the same baryon physics model, the posterior distributions of the cosmological parameters are found to be in excellent agreement with the true parameters values (within $10\%$ deviations in $\gtrsim 75\%$ and $\gtrsim 90\%$ of the cases for $Ω_m$ and $σ_8$, and a precision better than $10\%$ in both), while the astrophysical parameters are generally unconstrained due to the limited probed volume. When training on one model and testing on the other (e.g., training on IllustrisTNG and testing on SIMBA, or viceversa), the performance is significantly worse, both in accuracy and in precision, resulting in a $\sim 10\%$ positive bias on the predicted values for $σ_8$. We show that a multi-domain training based on the combination of simulations from both models recovers unbiased constraints, offering an effective solution to cope with the complex problem of the lack of convergence in the predictions from different galaxy formation models. This study represents a promising way forward to constrain cosmology and fundamental physics with the Lyman-$α$ forest with artificial intelligence.

Figures (22)

• Figure 1: Top: Mean flux $\bar{F}$ as a function of redshift, for IllustrisTNG (blue solid) and SIMBA (orange dashed), averaged over all the $1,000$ available simulations and with shaded regions indicating the standard deviation. Bottom: Mean flux ratios between SIMBA and IllustrisTNG, as a function of redshift.
• Figure 2: Comparison of $P_{\rm 1D}(k)$ from pairs of realizations with approximately same cosmology (within the same latin hypercube voxel), but different astrophysical parameters, at $z=2.00$ (top), $z=2.80$ (mid), $z=3.49$ (bottom) and. Per each redshift, we show the power spectra in the top sub-row, and the ratios with respect to one of the $P_{\rm 1D}(k)$ in the bottom sub-row, where the gray shaded region indicate the $10\%$ deviation region. Left: $P_{\rm 1D}(k)$ for realizations $31$ (blue solid) and $32$ (orange dashed), both from IllustrisTNG. Center: $P_{\rm 1D}(k)$ from realizations $85$ (blue solid) and $86$ (orange dashed), both from SIMBA. Right: $P_{\rm 1D}(k)$ from IllustrisTNG realization $54$ (blue solid), from SIMBA realization $86$ (orange dashed), and from SIMBA realization $86$ but including mean flux rescaling (green dotted).
• Figure 3: Ratios between the $P_{\rm 1D}(k)$ at $z=2$ from sets of six simulations varying only one astrophysical parameter, and their average, for IllustrisTNG (top set of plots) and SIMBA (bottom set of plots). Per each set of plots, we vary $A_{\rm SN1}$ in the top left panel, $A_{\rm AGN1}$ in the bottom left panel, $A_{\rm SN2}$ in the top right panel, and $A_{\rm AGN2}$ in the bottom right panel.
• Figure 4: Standard deviation of the $P_{\rm 1D}(k)$ from the $27$ CV realizations at $z=2.00$ (blue), $z=2.80$ (orange), and $z=3.49$ (green), for IllustrisTNG (left) and SIMBA (right).
• Figure 5: Graphical representation of the full workflow underlying this work. Top: extraction of the Ly$\alpha$ forest and computation of the $P_{\rm 1D}(k)$. Mid: input/output setup of the neural network. Bottom: schematic representation of the normalizing flow.