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

Reconstructing the initial conditions of the Universe from late-time tracers would unlock cosmological information buried by non-linear structure formation and astrophysics. The new analysis still awaits peer review, but it already lays out the central claim clearly.

It matters because cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. 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.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

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. This is further confirmed using Kullback-Leibler divergence diagnostics for an ensemble of observations.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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