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 corresponding to z = 300, with its linear amplitude extrapolated to z = 0, from simulated 21-cm and CO(1–0) line-intensity maps at z = 8 generated with the semi-numerical code, LIMFAST. Using a three-dimensional U-Net, we reconstruct the initial conditions and evaluate their 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. We additionally train and evaluate the reconstruction on maps incorporating SKA1-Low– and COMAP-ERA–like instrumental response and thermal noise. In the noiseless case, combining both tracers delivers the most accurate reconstruction across ionisation states, with the cross-correlation coefficient between the reconstructed and true initial density fields, |C(k)| ≳ 0.90 for k ≲ 0.75 Mpc−1. With observational effects, small-scale information is degraded, but the joint reconstruction retains substantial large-scale coherence, with |C(k)| ≳ 0.70 for k ≲ 0.3 Mpc−1. To quantify the cosmological information gain, we perform simulation-based inference using power-spectrum summaries pre- and post-reconstruction. Across an ensemble of realisations, reconstruction yields the largest improvements for σ8 and ns, with a median aggregate marginal compression of 1.17 bits in the noiseless case, corresponding to a 56% reduction in the factorised product of prior-normalised 68% marginal widths. With observational effects, the corresponding median compression is 1.29 bits. These results demonstrate that joint 21-cm–CO reconstruction can recover cosmological information beyond that captured by the pre-reconstruction summaries.