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We constrain cold dark energy of negligible sound speed using galaxy clusterabundance observations. In contrast to standard quasi-homogeneous dark energy,negligible sound speed implies clustering of the dark energy fluid at allscales, allowing us to measure the effects of dark energy perturbations atcluster scales. We compare those models and set the stage for using non-linearinformation from semi-analytical modelling in cluster growth data analyses. Forthis, we recalibrate the halo mass function with non-linear characteristicquantities, the spherical collapse threshold and virial overdensity, thataccount for model and redshift dependent behaviours, as well as an additionalmass contribution for cold dark energy. We present the first constraints fromthis cold dark matter plus cold dark energy mass function using our clusterabundance likelihood, which self-consistently accounts for selection effects,covariances and systematic uncertainties. We combine cluster growth data withCMB, SNe Ia and BAO data, and find a shift between cold versusquasi-homogeneous dark energy of up to $1\sigma$. We make a Fisher matrixforecast of constraints attainable with cluster growth data from the on-goingDark Energy Survey (DES). For DES, we predict $\sim$50$\%$ tighter constraintson $\left(\Omega_\mathrm{m},w \right)$ for cold dark energy versus $w$CDMmodels, with the same free parameters. Overall, we show that cluster abundanceanalyses are sensitive to cold dark energy, an alternative, viable model thatshould be routinely investigated alongside the standard dark energy scenario.

Cold dark energy constraints from the abundance of galaxy clusters