Cosmological inference from combining Planck and ACT cluster counts

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 2016 sample from Planck and the 2018 sample from ACT we find, by fixing the cosmology using CMB 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 modeling parameter describing redshift dependence $\beta=0.86 \pm 0.07$ using an updated CCCP-based normalization, or evolution in the cosmological model quantified by the dark energy equation of state parameter $w=-0.82 \pm 0.07$.