Bounding the Effect of HOD Assumptions on Small-Scale Clustering Constraints

Small-scale galaxy clustering is expected to contain substantial cosmological information, but the extent to which this information constrains halo-based cosmologies independent of an assumed galaxy--halo connection remains unclear. The new analysis still awaits peer review, but it already lays out the central claim clearly.

This 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 quantify this dependence using LRG-like mock galaxy catalogs built from 81 cosmologies in the {\tt \textsc{AbacusSummit}} suite. We analyze two-point correlation function multipoles on scales ranging from $5$--$80$ Mpc/$h$ and compare two limiting treatments, the \enquote{floor} and \enquote{ceiling}, of.

In the conservative floor case, we impose only broad initial HOD bounds and profile over HOD parameters to determine the minimum constraining power available. We accomplish this with {\tt HODmin}, a two-stage global optimization algorithm written for minimizing $χ^2$ in HOD space.

In the optimistic ceiling case, we assume the HOD parameters are known exactly. We find a significant difference between the floor and ceiling when comparing against the same Planck $Λ$CDM mock data vector with identical modeling assumptions: for the floor.

Many cosmologies agree well with data in the floor, and yet in the ceiling are excluded by multiple orders of magnitude in $χ^2$. We therefore observe the strength of small-scale clustering constraints depends heavily on the amount of prior HOD information assumed.

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.

We compare the sensitivity of this effect to various choices like scale cut, angle cut, multipole inclusion, mock phase, and mock HOD model. Our wide floor--ceiling bracket indicates that informative galaxy--halo priors are necessary for extracting strong small-scale clustering constraints.

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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