Abstract
Aims. We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey. Methods. By analysing 1000 Euclid-like light cones, produced with the PINOCCHIO approximate method, we validated the analytical model of Hu & Kravtsov (2003, ApJ, 584, 702) for the covariance matrix, which takes into account both sources of statistical error. Then, we used such a covariance to define the likelihood function that is better equipped to extract cosmological information from cluster number counts at the level of precision that will be reached by the future Euclid photometric catalogs of galaxy clusters. We also studied the impact of the cosmology dependence of the covariance matrix on the parameter constraints. Results. The analytical covariance matrix reproduces the variance measured from simulations within the 10 percent; such a difference has no sizeable effect on the error of cosmological parameter constraints at this level of statistics. Also, we find that the Gaussian likelihood with full covariance is the only model that provides an unbiased inference of cosmological parameters without underestimating the errors, and that the cosmology-dependence of the covariance must be taken into account.
Highlights
Galaxy clusters are the most massive gravitationally bound systems in the Universe (M ∼ 1014−1015 M ) of which dark matter makes up about 85 percent, hot ionized gas 12 percent, and stars 3 percent (Pratt et al 2019)
The former case indicates the presence of systematics due to an incorrect analysis, while the latter suggests that not all the relevant sources of error have been taken into account
In this work, we study some of the theoretical systematics that can affect the derivation of cosmological constraints from the analysis of number counts of galaxy clusters from a survey with its sky-coverage and selection function similar to what is expected for the photometric Euclid cluster survey
Summary
Galaxy clusters are the most massive gravitationally bound systems in the Universe (M ∼ 1014−1015 M ) of which dark matter makes up about 85 percent, hot ionized gas 12 percent, and stars 3 percent (Pratt et al 2019). Clusters can be observed at low redshift (out to redshift z ∼ 2), sampling the cosmic epochs during which the effect of dark energy begins to dominate the expansion of the Universe; as such, the evolution of the statistical properties of galaxy clusters should allow us to place constraints on the dark energy equation of state, and detect possible deviations of dark energy from a simple cosmological constant (Sartoris et al 2012). To quantify the contribution of these effects, an accurate statistical analysis is required, which is to be performed on a large number of realizations of past light cones extracted from cosmological simulations describing the distribution of cluster-sized halos. This is made possible using approximate methods for such simulations (e.g., Monaco 2016). While this paper is focused on the analysis relevant for a cluster survey similar in sky coverage and depth to that of Euclid, for completeness, we provide in Appendix B those results that are relevant for present and ongoing surveys
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