In this paper we present a power spectrum formalism that combines the full
three-dimensional 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 polarisation data; including the inter-datum power
spectra between all quantities. We apply this to forecasting cosmological
parameter errors for CMB and imaging surveys for Euclid-like, Planck, ACTPoL,
and CoRE-like experiments. We show that the additional covariance between the
CMB and ellipticity measurements can improve dark energy equation of state
measurements by 15%, and 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.Comment: Accepted to MNRA
