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.
