Cosmological analysis of three-dimensional BOSS galaxy clustering and Planck CMB lensing cross correlations via Lagrangian perturbation theory

We present a formalism for jointly fitting pre-and post-reconstruction redshift-space clustering (RSD) and baryon acoustic oscillations (BAO) plus gravitational lensing (of the CMB) that works directly with the observed 2-point statistics. The formalism is based upon (effective) Lagrangian perturbation theory and a Lagrangian bias expansion, which models RSD, BAO and galaxy-lensing cross correlations within a consistent dynamical framework. As an example we present an analysis of clustering measured by the Baryon Oscillation Spectroscopic Survey in combination with CMB lensing measured by Planck. The post-reconstruction BAO strongly constrains the distance-redshift relation, the full-shape redshift-space clustering constrains the matter density and growth rate, and CMB lensing constrains the clustering amplitude. Using only the redshift space data we obtain omega(m) = 0.303 +/- 0.008, H-0 = 69.21 +/- 0.78 and sigma(8) = 0.743 +/- 0.043. The addition of lensing information, even when restricted to the Northern Galactic Cap, improves constraints to omega(m)= 0.300 +/- 0.008, H-0 = 69.21 +/- 0.77 and sigma(8) = 0.707 +/- 0.035, in tension with CMB and cosmic shear constraints. The combination of S2m and H0 are consistent with Planck, though their constraints derive mostly from redshift-space clustering. The low sigma(8) value are driven by cross correlations with CMB lensing in the low redshift bin (z (sic) 0.38) and at large angular scales, which show a 20% deficit compared to expectations from galaxy clustering alone. We conduct several systematics tests on the data and find none that could fully explain these tensions.

Automated summary

We propose a formalism for jointly fitting pre-and post-reconstruction redshift-space clustering, baryon acoustic oscillations, and gravitational lensing. We analyze clustering measured by the Baryon Oscillation Spectroscopic Survey in combination with CMB lensing measured by Planck. The results provide valuable constraints on various cosmological parameters.