The next generation of space surveys in cosmology and galaxy evolution will focus on the questions that Euclid, the Roman Space Telescope and the Legacy Survey of Space and Time (LSST) will not resolve.

The covariance of galaxy clusters is an important element when constraining cosmology with galaxy clusters. However its computation is costly in computational resources, especially when it depends on cosmology. We propose an evaluation of the impact on the cosmological parameters when the modeling of the cluster covariance is simplified. This is one of the projects for the preparation of the LSST-DESC cluster cosmology framework.