Description:
Recently, it has been shown that cross-correlating CMB lensing and 3D cosmic shear allows to considerably tighten cosmological parameter constraints. We investigate whether similar improvement can be achieved in a conventional tomographic setup. We present Fisher parameter forecasts for a Euclid-like galaxy survey in combination with different ongoing and forthcoming CMB experiments. In contrast to a fully three-dimensional analysis we find only marginal improvement. Assuming Planck-like CMB data we show that including the full covariance of the combined CMB and cosmic shear data improves the dark energy figure of merit by only three per cent. The marginalized error on the sum of neutrino masses is reduced at the same level. For a next generation CMB satellite mission such as Prism the predicted improvement of the dark energy figure of merit amounts to approximately 25 per cent. Furthermore, we show that the small improvement is contrasted by an increased bias in the dark energy parameters when the intrinsic alignment of galaxies is not correctly accounted for in the full covariance matrix.