Cosmology-dependent covariance in galaxy cluster number counts: consequences for parameter inference

Galaxy clusters provide constraints on cosmology through their abundance as a function of mass and redshift. Parameter inference from cluster counts requires modelling the covariance entering the likelihood, including contributions from. 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. Parameter inference from cluster counts requires modelling the covariance entering the likelihood, including contributions from Poisson shot noise and super-sample covariance. Since evaluating the full covariance during parameter inference can be computationally expensive, particularly for SSC terms, many analyses compute it at a fiducial cosmology and.

In this work, we investigate the impact of covariance misspecification on the estimation of $Ω_c$, $σ_8$, and $w$. We perform a systematic analysis in which the covariance is either varied consistently with the sampled cosmology or fixed at displaced cosmological models, including intermediate.

Our analysis incorporates observational effects relevant for LSST-like optical surveys, including mass-proxy scatter and photometric redshift uncertainties. We find that the estimators of $Ω_c$, $σ_8$, and $w$ remain unbiased even when the covariance is evaluated at an incorrect cosmology.

The magnitude and sign of this effect are driven primarily by amplitude-related parameters such as $S_8$. For LSST-like surveys, an inconsistent covariance specification can artificially modify the apparent $S_8$ tension inferred from cluster counts.

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 further show that a single covariance update evaluated at the recovered best-fit cosmology is sufficient to restore the correct uncertainty normalization. These results indicate that fixed-covariance approximations may be adequate for some single-probe analyses, but a fully cosmology-dependent treatment is required for consistent.

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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