3D weak gravitational lensing of the CMB and galaxies

In this paper, we present a power spectrum formalism that combines the full 3D information from the galaxy ellipticity field, with information from the cosmic microwave background (CMB). We include in this approach galaxy cosmic shear and galaxy intrinsic alignments, CMB deflection, CMB temperature, and CMB polarization data; including the interdatum power spectra between all quantities. We apply this to forecasting cosmological parameter errors for CMB and imaging surveys and show that the additional covariance between the CMB and ellipticity measurements can improve dark energy equation of state measurements by 30 per cent. We present predictions for Euclid-like, Planck, ACTPoL, and CoRE-like experiments and show that the combination of cosmic shear and the CMB, from Euclid-like and CoRE-like experiments, could in principle measure the sum of neutrino masses with an error of 0.003 eV, and the dark energy equation of state with an error on w0 of less than 0.02.