Improving cosmological distance measurements at high redshift using Lyman-Alpha forest BAO reconstruction

The Dark Energy Spectroscopic Instrument measures baryon acoustic oscillations in the Lyman-$α$ forest and provides a robust probe of the expansion history in the matter-dominated era. 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. The Dark Energy Spectroscopic Instrument (DESI) measures baryon acoustic oscillations (BAO) in the Lyman-$α$ (Lyman-alpha) forest and provides a robust probe of the expansion. Yet, non-linear structure formation broadens and shifts the BAO peak.

To undo these effects, we extend standard Zel'dovich reconstruction, routinely applied to galaxy surveys, to the Lyman-alpha forest. We validate our methodology on large-volume idealized Lyman-alpha forest mocks painted on top of the \textsc{AbacusSummit} $N$-body simulations, using linear control variates to.

In fully sampled periodic boxes, reconstruction halves the radial BAO damping scale and reduces the uncertainties on the radial ($\apar$) and transverse ($\aperp$) scaling. It also reduces the non-linear shift from $Δ\apar=+0.3\%$ to $+0.10\pm0.07\%$, while $\aperp$ remains unbiased.

To make this approach readily applicable to observational data, we demonstrate the impact of a survey mask with a DESI-like density of $50\, \mathrm{deg}^{-2}$. For this mask, we compare two approaches to estimate the displacement field: either directly from the Lyman-alpha forest or using an external tracer with a number density of $\bar.

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.

Both approaches give comparable gains and reduce the uncertainties on $\apar$ and $\aperp$ by $\approx 27\%$ and $\approx 10\%$, respectively, with mild improvements for. Correspondingly, the figure of merit improves by factors of $1.66$ for fully sampled boxes, $1.65$ for a DESI-like, and $1.76$ for a high-density survey.

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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