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

We forecast the sensitivity of ongoing and future galaxy cluster abundance measurements to detect deviations from the cold dark matter (CDM) paradigm. Concretely, we consider a class of dark sector models that feature an interaction between dark matter and a dark radiation species (IDM-DR). This setup can be naturally realized by a non-Abelian gauge symmetry and has the potential to explain S8 tensions arising within Lambda CDM. We create mock catalogs of the ongoing SPT-3G as well as the future CMB-S4 surveys of galaxy clusters selected via the thermal Sunyaev-Zeldovich effect (tSZE). Both datasets are complemented with cluster mass calibration from next-generation weak gravitational lensing data (ngWL) like those expected from the Euclid mission and the Vera C. Rubin Observatory. We consider an IDM-DR scenario with parameters chosen to be in agreement with Planck 2018 data and that also leads to a low value of S8 as indicated by some local structure formation analyses. Accounting for systematic and stochastic uncertainties in the mass determination and the cluster tSZE selection, we find that both SPT-3G x ngWL and CMB-S4 x ngWL cluster data will be able to discriminate this IDM-DR model from Lambda CDM, and thus test whether dark matter-dark radiation interactions are responsible for lowering S8. Assuming IDM-DR, we forecast that the temperature of the dark radiation can be determined to about 40% (10%) with SPT-3G x ngWL (CMB-S4 x ngWL), considering 68% credibility, while S8 can be recovered with percent-level accuracy. Furthermore, we show that IDM-DR can be discriminated from massive neutrinos, and that cluster counts will be able to constrain the dark radiation temperature to be below similar to 10% (at 95% credibility) of the cosmic microwave background temperature if the true cosmological model is Lambda CDM.