Recent progress in observational cosmology and the establishment of ΛCDM have relied on the combination of different cosmological probes. These probes are not independent, since they all measure the same physical fields. The resulting cross-correlations allow for a robust test of the cosmological model through the consistency of different physical tracers and for the identification of systematics. Integrated analyses, taking into account both the auto- as well as the cross-correlations between cosmological probes, therefore present a promising analysis method for both current as well as future data.
In this talk, I will present an integrated analysis of CMB temperature anisotropies, CMB lensing, galaxy clustering and weak lensing as well as background probes. I will describe the cosmological probe combination framework, the obtained results and illustrate how this analysis has provided a confirmation of ΛCDM through the consistency of different probes. Furthermore, I will discuss possible tensions between the derived constraints on cosmological parameters and existing ones.