Integrated approach to cosmology: Combining CMB, large-scale structure and weak lensing

Recent observational progress has led to the establishment of the standard $\Lambda$CDM model for cosmology. This development is based on different cosmological probes that are usually combined through their likelihoods at the latest stage in the analysis. We implement here an integrated scheme for cosmological probes, which are combined in a common framework starting at the map level. This treatment is necessary as the probes are generally derived from overlapping maps and are thus not independent. It also allows for a thorough test of the cosmological model and of systematics through the consistency of different physical tracers. As a first application, we combine current measurements of the Cosmic Microwave Background (CMB) from the Planck satellite, and galaxy clustering and weak lensing from SDSS. We consider the spherical harmonic power spectra of these probes including all six auto- and cross-correlations along with the associated full Gaussian covariance matrix. This provides an integrated treatment of different analyses usually performed separately including CMB anisotropies, cosmic shear, galaxy clustering, galaxy-galaxy lensing and the Integrated Sachs-Wolfe (ISW) effect with galaxy and shear tracers. We derive constraints on $\Lambda$CDM parameters that are compatible with existing constraints and highlight tensions between data sets, which become apparent in this integrated treatment. We discuss how this approach provides a complete and powerful integrated framework for probe combination and how it can be extended to include other tracers in the context of current and future wide field cosmological surveys.
Comment: 29 pages, 19 figures, 3 tables, to appear in PRD, updated following referee's comments including small changes in results