Tracing the Cosmic Origins: Machine Learning Reconstruction of the Primordial Density Field from EoR Observations

Abstract

Reconstructing the initial conditions of the Universe from late-time tracers would unlock cosmological information buried by non-linear structure formation and astrophysics. We reconstruct the initial density field at $z\sim300$ from simulated 21-cm and CO(1-0) line-intensity maps at $z\sim8$ generated with LIMFAST. Using a three-dimensional U-Net, we reconstruct the initial conditions and evaluate its impact on cosmological parameter constraints. The two tracers probe complementary environments: 21-cm emission traces neutral, low-density regions of the intergalactic medium, while CO traces overdense, star-forming regions. To emulate realistic observations, we model instrumental effects for SKA1-Low- and COMAP-ERA-like surveys, including finite angular resolution and thermal noise. We assess reconstruction performance through the cross-correlation coefficient between reconstructed and true initial density fields, $|C(k)|$. In the noiseless case, combining both tracers delivers the most accurate recovery across ionisation states, with $|C(k)| \gtrsim$ 0.90 for $k \lesssim$ 0.75 Mpc$^{-1}$. With observational effects, small-scale information is degraded, but combining tracers still achieves $|C(k)| \gtrsim$ 0.70 for $k \lesssim$ 0.3 Mpc$^{-1}$. To quantify information gain, we perform simulation-based inference of cosmological parameters from power-spectrum summaries before and after reconstruction. In both noiseless and noisy settings, reconstruction tightens parameter constraints: uncertainties on $σ_8$ and $n_{\rm s}$ improve by $\sim2\times$, with smaller but consistent gains for other parameters. This is further confirmed using Kullback-Leibler divergence diagnostics for an ensemble of observations. These results indicate that joint analysis of future 21-cm and CO surveys, combined with such reconstruction, can partially recover otherwise inaccessible cosmological information.