We present the first joint analysis of cluster abundances and auto or cross-correlations of three cosmic tracer fields: galaxy density, weak gravitational lensing shear, and cluster density split by optical richness. From a joint analysis ($4\times 2\mathrm{pt}+\mathrm{N}$) of cluster abundances, three cluster cross-correlations, and the auto correlations of the galaxy density measured from the first year data of the Dark Energy Survey, we obtain ${\mathrm{\Omega }}_m=0.305_{-0.038}^{+0.055}$ and ${\sigma }_8=0.783_{-0.054}^{+0.064}$. This result is consistent with constraints from the DES-Y1 galaxy clustering and weak lensing two-point correlation functions for the flat $\nu \mathrm{\Lambda }\mathrm{CDM}$ model. Consequently, we combine cluster abundances and all two-point correlations from across all three cosmic tracer fields ($6\times 2\mathrm{pt}+\mathrm{N}$) and find improved constraints on cosmological parameters as well as on the cluster observable-mass scaling relation. This analysis is an important advance in both optical cluster cosmology and multiprobe analyses of upcoming wide imaging surveys.

• Received 6 October 2020
• Revised 7 January 2021
• Accepted 23 February 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.141301