Exploring Cosmic Origins with CORE: Cluster Science
  We examine the cosmological constraints that can be achieved with a galaxy
cluster survey with the future CORE space mission. Using realistic simulations
of the millimeter sky, produced with the latest version of the Planck Sky
Model, we characterize the CORE cluster catalogues as a function of the main
mission performance parameters. We pay particular attention to telescope size,
key to improved angular resolution, and discuss the comparison and the
complementarity of CORE with ambitious future ground-based CMB experiments that
could be deployed in the next decade. A possible CORE mission concept with a
150 cm diameter primary mirror can detect of the order of 50,000 clusters
through the thermal Sunyaev-Zeldovich effect (SZE). The total yield increases
(decreases) by 25% when increasing (decreasing) the mirror diameter by 30 cm.
The 150 cm telescope configuration will detect the most massive clusters
($>10^{14}\, M_\odot$) at redshift $z>1.5$ over the whole sky, although the
exact number above this redshift is tied to the uncertain evolution of the
cluster SZE flux-mass relation; assuming self-similar evolution, CORE will
detect $\sim 500$ clusters at redshift $z>1.5$. This changes to 800 (200) when
increasing (decreasing) the mirror size by 30 cm. CORE will be able to measure
individual cluster halo masses through lensing of the cosmic microwave
background anisotropies with a 1-$\sigma$ sensitivity of $4\times10^{14}
M_\odot$, for a 120 cm aperture telescope, and $10^{14} M_\odot$ for a 180 cm
one. [abridged]
