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We forecast the sensitivity of ongoing and future galaxy cluster abundancemeasurements to detect deviations from the cold dark matter (CDM) paradigm.Concretely, we consider a class of dark sector models that feature aninteraction between dark matter and a dark radiation species (IDM-DR). Thissetup can be naturally realized by a non-Abelian gauge symmetry and has thepotential to explain $S_8$ tensions arising within $\Lambda$CDM. We create mockcatalogs of the ongoing SPT-3G as well as the future CMB-S4 surveys of galaxyclusters selected via the thermal Sunyaev-Zeldovich effect (tSZE). Bothdatasets are complemented with cluster mass calibration from next-generationweak gravitational lensing data (ngWL) like those expected from the Euclidmission and the Vera C. Rubin Observatory. We consider an IDM-DR scenario withparameters chosen to be in agreement with Planck 2018 data and that also leadsto a low value of $S_8$ as indicated by some local structure formationanalyses. Accounting for systematic and stochastic uncertainties in the massdetermination and the cluster tSZE selection, we find that bothSPT-3G$\times$ngWL and CMB-S4$\times$ngWL cluster data will be able todiscriminate this IDM-DR model from $\Lambda$CDM, and thus test whether darkmatter - dark radiation interactions are responsible for lowering $S_8$.Assuming IDM-DR, we forecast that the temperature of the dark radiation can bedetermined to about 40% (10%) with SPT-3G$\times$ngWL (CMB-S4$\times$ngWL),considering 68% credibility, while $S_8$ can be recovered with percent-levelaccuracy. Furthermore, we show that IDM-DR can be discriminated from massiveneutrinos, and that cluster counts will be able to constrain the dark radiationtemperature to be below $\sim 10%$ (at 95% credibility) of the cosmic microwavebackground temperature if the true cosmological model is $\Lambda$CDM.

Probing interacting dark sector models with future weak lensing-informed galaxy cluster abundance constraints from SPT-3G and CMB-S4