Joint galaxy-lensing observables and the dark energy

Deep multicolor galaxy surveys with photometric redshifts will provide a large number of two-point correlation observables: galaxy-galaxy angular correlations, galaxy-shear cross correlations, and shear-shear correlations between all redshifts. These observables can potentially enable a joint determination of the dark-energy-dependent evolution of the dark matter and distances as well as the relationship between galaxies and dark matter halos. With recent cosmic microwave background determinations of the initial power spectrum, a measurement of the mass clustering at even a single redshift will constrain a well-specified combination of dark energy (DE) parameters in a flat universe; we provide convenient fitting formulas for such studies. The combination of galaxy-shear and galaxy-galaxy correlations can determine this amplitude at multiple redshifts. We illustrate this ability in a description of the galaxy clustering with 5 free functions of redshift which can be fitted from the data. The galaxy modeling is based on a mapping onto halos of the same abundance that models a flux-limited selection. In this context and under a flat geometry, a 4000 deg${}^2$ galaxy-lensing survey can achieve a statistical precision of $\sigma \left({\Omega }_{\mathrm{DE}}\right)=0.005\mathrm{}$ for the dark energy density, $\sigma {(w}_{\mathrm{DE}})=0.02\mathrm{}$ and $\sigma {(w}_a)=0.17\mathrm{}$ for its equation of state and evolution, evaluated at dark energy matter equality $z\approx 0.4,$ as well as constraints on the 5 halo functions out to $z=1.\mathrm{}$ More importantly, a joint analysis can make dark energy constraints robust against systematic errors in the shear-shear correlation and halo modeling.