Field-level Reconstruction from Foreground-Contaminated 21-cm Maps

TL;DR

This paper tackles recovering large-scale 21-cm density modes hidden by foreground wedges in interferometric data. It develops two complementary reconstruction pathways: (i) field-level inference within an effective field theory framework using gradient-based sampling (MCLMC) to jointly infer initial conditions and bias parameters, and (ii) a variational diffusion model trained on simulations to generate posterior reconstructions conditioned on wedge-filtered observations. On EFT-generated mocks, the EFT-based method provides tighter large-scale constraints, while the diffusion model yields comparable results with broader uncertainties and greater flexibility to varying wedge configurations; on more realistic 21cmFAST mocks, the EFT approach remains slightly superior but diffusion remains competitive. The results demonstrate that wedge reconstruction can markedly enhance cosmological information and enable robust cross-correlations across experiments, with potential for hybrid approaches that fuse physical modeling and deep generative techniques to optimize information recovery.

Abstract

Current and upcoming 21-cm experiments will soon be able to map 21-cm spatial fluctuations in three dimensions for a wide range of redshifts. However, bright foreground contamination and the nature of radio interferometry create significant challenges, making it difficult to access rich cosmological information from the Fourier modes that lie within the "foreground wedge". In this work, we introduce two approaches aiming to reconstruct the full 21-cm density field, including the missing modes in the wedge: (a) a field-level inference under an effective field theory (EFT) framework; (b) a diffusion-based deep generative model trained on simulations. Under the EFT framework, we implement a fully differentiable forward model that maps the initial conditions of matter fluctuations to the observed, foreground-filtered 21-cm maps. This enables a gradient-based sampler to simultaneously sample the initial conditions and bias parameters, allowing a physically motivated mode reconstruction. Alternatively, we apply a variational diffusion model to perform 21-cm density reconstruction at the map level. Our model is trained on semi-numerical simulations over a wide range of astrophysical parameters. Our results from both approaches should provide improved cosmological constraints from the field level and also enable cross-correlation between experiments that have little or no overlapping modes.

Figures (9)

• Figure 1: Examples of the true (left column) and foreground-filtered (right column) 21-cm fields generated from 21cmFAST. The top row shows the 21-cm field in the plane perpendicular to the line of sight, while the $z$-axis in the bottom row indicates the line-of-sight direction. The foreground filter significantly distorts the line-of-sight axis in order to remove the spectrally smooth foreground contamination.
• Figure 2: Foreground-filtered 21-cm signal and noise in Fourier space (left) and coordinate space (right). The left panel shows the spherically averaged power spectrum as a function of Fourier modes $k$; the right panel shows a slice of 21-cm field along a spatial coordinate. The green dots are from 21cmFAST using the astrophysical parameters given in \ref{['tab:21cmFASTTrainingParamRange']}; the solid black lines are obtained by fitting an effective field theory model to the 21cmFAST data at the field level, given the underlying matter density field; the dotted lines indicate the noise level assumed in this work. The result on the right panel is smoothed beyond $k\sim 0.8\,h/$Mpc, a scale at which we assume the effective field theory framework becomes invalid.
• Figure 3: Renormalized bias parameters inferred from foreground-filtered, EFT-generated 21-cm field. The dashed lines show the fiducial values of the bias parameters (see Eq. \ref{['eq:fiducial_bias']}), and the contours indicate the 68% and 95% confidence regions for the posterior distribution. The orange contours correspond to the field-level fit as described in Section \ref{['subsec:implement_HMC']}, while the green contours are obtained by fitting only 2-pt and 3-pt summary statistics---the power spectrum monopole and the skew spectra (c.f. Section \ref{['subsec:summary_statistics']}). As the field-level fit also constrains the initial density field, we show the posterior distributions for three pixels in real space as an example. Here, Pixel A and B are next to each other, while Pixel C lies $\sim$50 comoving $\mathrm{Mpc}/h$ away. For reference, the dashed gray curves indicate the standard normal priors assumed for each pixel.
• Figure 4: Configuration-space reconstructions using the gradient-based method on the foreground-filtered, EFT-generated 21-cm field. The top left corner shows a slice of the input 21-cm field with modes within the foreground wedge removed. Our gradient-based sampler is applied directly to this input to sample both the bias parameters (see \ref{['fig:recovery_eftbias']}) and the initial density field. The bottom left panel shows the reconstructed density field, marginalized over bias parameters. Each joint sample of the bias parameters and the initial density field is then used to generate a 21-cm field, as can be seen in the middle panel on the top row. These maps are $500$ comoving $\mathrm{Mpc}/h$ on the side and we also zoom in to a $100\times100$ comoving $(\mathrm{Mpc}/h)^2$ area to see the performance of our method on small scales.
• Figure 5: Validation tests of the gradient-based method on the foreground-filtered, EFT-generated 21-cm field. Left: Cross-correlation between the true underlying 21-cm field and the reconstructed 21-cm field; Middle: Cross-correlation between the true underlying initial density condition and the reconstructed one; Right: Spherically averaged cross-correlations (upper panel) and transfer functions (lower panel) between the true and reconstructed 21-cm (orange) and underlying initial density condition (purple) fields (see \ref{['eq:recon_statistics']}). Shaded regions denote the 68% credible intervals from 100 posterior samples.