Combining cluster number counts and galaxy clustering
The abundance of clusters and the clustering of galaxies are two of the important cosmological probes for current and future large scale surveys of galaxies, such as the Dark Energy Survey. In order to combine them one has to account for the fact that they are not independent quantities, since they probe the same density field. It is important to develop a good understanding of their correlation in order to extract parameter constraints. We present a detailed modelling of the joint covariance matrix between cluster number counts and the galaxy angular power spectrum. We employ the framework of the halo model complemented by a Halo Occupation Distribution model (HOD). We demonstrate the importance of accounting for non-Gaussianity to produce accurate covariance predictions. Indeed, we show that the non-Gaussian covariance becomes dominant at small scales, low redshifts or high cluster masses. We discuss in particular the case of the super-sample covariance (SSC), including the effects of galaxy shot-noise, halo second order bias and non-local bias. We demonstrate that the SSC obeys mathematical inequalities and positivity. Using the joint covariance matrix and a Fisher matrix methodology, we examine the prospects of combining these two probes to constrain cosmological and HOD parameters. We find that the combination indeed results in noticeably better constraints, with improvements of order 20% on cosmological parameters compared to the best single probe, and even greater improvement on HOD parameters, with reduction of error bars by a factor 1.4-4.8. This happens in particular because the cross-covariance introduces a synergy between the probes on small scales. We conclude that accounting for non-Gaussian effects is required for the joint analysis of these observables in galaxy surveys.