MujicΛ: Reconstructing Initial Conditions from Incomplete Redshift Surveys with Projected Optimization

In this paper, we introduce MujicΛ, an optimization-based framework for reconstructing initial conditions from realistic galaxy spectroscopic redshift surveys. The new analysis still awaits peer review, but it already lays out the central claim clearly.

It is relevant 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. Unlike standard optimization-based approaches, MujicΛ augments the L-BFGS algorithm with a projection operator and rank-order matching to enforce Gaussianity of the initial. In this paper, we introduce MujicΛ (Mapping the Universe with Jax-based Initial Condition ReconstrΛction), an optimization-based framework for reconstructing initial conditions.

We validate MujicΛ on a mock lightcone catalog derived from semi-analytic models applied to the Millennium simulation. We construct a differentiable forward model that incorporates a fast particle-mesh simulation at megaparsec resolution and a comprehensive treatment of observational effects and.

MujicΛ reaches good agreement with the true density field down to the scale of the forward model, while maintaining consistency with the Gaussian prior through the projection step. It also broadly recovers the cosmic web classification, underscoring its value for deciphering environmental information in galaxy evolution studies.

Beyond its key role in next-generation constrained simulations, the methodology offers a practical way to generate initial guesses and speed up field-level inference, especially. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

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.

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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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