Cosmological inference from combining <i>Planck</i> and ACT cluster counts

ABSTRACT We have adapted the Planck cluster likelihood in such a way that it can be applied to the sample of clusters detected by the Atacama Cosmology Telescope (ACT). Applying it to the Planck sample from 2016 and the ACT sample from 2018, we find, by fixing the cosmology using cosmic microwave background observations and the cluster model adopted by Planck, that the mass bias required by the two are $1-b_{\rm Planck}=0.61\pm 0.03$ and $1-b_{\rm ACT}=0.75\pm 0.06$. These are broadly in agreement but hint that the model could be adapted to reach a better agreement. By normalizing the cluster model using weak lensing observations, we find evidence for either evolution in the cluster model, quantified by the cluster modelling parameter describing redshift dependence $\beta =0.86 \pm 0.07$ using an updated Canadian Cluster Comparison Project (CCCP)-based normalization, or evolution in the cosmological model quantified by the dark energy equation-of-state parameter $w=-0.82 \pm 0.07$.