AMICO galaxy clusters in KiDS-1000: Cosmological constraints from the two-point correlation function

In this paper we study the clustering properties of an optically identified photometric galaxy cluster catalogue from KiDS-1000. The sample was identified by the AMICO algorithm and consists of 9049 clusters with $S/N\geq3. 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. Clusters are selected according to their observed intrinsic richness, with thresholds of $λ^*{obs}\geq 20, 25, 30$ within $0.10\leq z<0.30$, $0. The sample was identified by the AMICO algorithm and consists of 9049 clusters with $S/N\geq3.5$, in the redshift range $0.1\leq z<0.8$, spread over an effective area of 838.

Clusters are selected according to their observed intrinsic richness, with thresholds of $λ^*{obs}\geq 20, 25, 30$ within $0.10\leq z<0.30$, $0.30\leq z<0.45$ and $0.45\leq z<0. We measure the multipoles of the two-point correlation function over different ranges of scales from 5 $h^{-1}$ Mpc to 150 $h^{-1}$ Mpc.

We model the clustering signal in the context of the $Λ$CDM cosmology, accounting for the main observational effects, such RSDs and photo-$z$ uncertainties. The effective bias of the cluster sample is estimated via a mass-richness scaling relation.

For the MCMC analysis, we adopt Gaussian priors on the parameters of the mass-richness scaling relation, and broad, uniform priors to derive cosmological constraints on the cold. Specifically, we find $Ω_{m}=0.24^{+0.02}{-0.02}$ and $σ_8=0.86^{+0.13}{-0.10}$ representing an improvement in precision over both the 2D and 3D AMICO clustering analyses.

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.

Moreover, we obtain $S_8=0.77^{+0.10}_{-0.08}$ in $1σ$ agreement with the AMICO KiDS-1000 number counts constraints estimated from the same catalogue, as well as with some results. Our work strengthens the potential of cluster clustering as a complementary and competitive probe, to be included and further developed with the final KiDS-Legacy data release.

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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