Cosmological constraints from a joint analysis of cosmic microwave background and large-scale structure

The standard model of cosmology, $\Lambda$CDM, is the simplest model that matches the current observations, but relies on two hypothetical components, to wit, dark matter and dark energy. Future galaxy surveys and cosmic microwave background (CMB) experiments will independently shed light on these components, but a joint analysis that includes cross-correlations will be necessary to extract as much information as possible from the observations. In this paper, we aim at developing the methods needed to perform such an analysis, and test it on publicly available data sets. In particular, we use CMB temperature anisotropies and CMB lensing observations from Planck, and the spectroscopic galaxy and quasar samples of SDSS-III/BOSS. We build a likelihood to simultaneously analyse the auto and cross spectra of the CMB lensing and the galaxy overdensity maps before running Monte-Carlo Markov Chains (MCMC) to assess the constraining power of the combined analysis. We then add CMB temperature information and run MCMCs to test the $\Lambda$CDM model. We present constraints on cosmological parameters and galaxy biases, and demonstrate that the joint analysis can additionally constrain the mass of neutrinos as well as the dark energy equation of state. Finally, we discuss several difficulties regarding the analysis itself and the theoretical precision of the models, which will require additional work to properly analyse the observations of the next generation of cosmological experiments.