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

The standard model of cosmology, {Lambda}CDM, is the simplest model that matches the current observations, but it 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 carry out a multi-probe analysis based on pseudo-spectra and test it on publicly available data sets. We use CMB temperature anisotropies and CMB lensing observations from Planck as well as the spectroscopic galaxy and quasar samples of SDSS-III/BOSS, taking advantage of the large areas covered by these surveys. We build a likelihood to simultaneously analyse the auto and cross spectra of CMB lensing and tracer overdensity maps before running Monte-Carlo Markov Chains (MCMC) to assess the constraining power of the combined analysis. We then add the CMB temperature anisotropies likelihood and obtain constraints on cosmological parameters ($H_0$, $omega_b$, $omega_c$, ${ln10^{10}A_s}$, $n_s$ and $z_{re}$) and galaxy biases. We demonstrate that the joint analysis can additionally constrain the total mass of neutrinos ${Sigma m_{ u}}$ as well as the dark energy equation of state $w$ at once (for a total of eight cosmological parameters), which is impossible with either of the data sets considered separately. Finally, we discuss limitations of the analysis related to, e.g., the theoretical precision of the models, particularly in the non-linear regime.