Dark energy and neutrino masses from future measurements of the expansion history and growth of structure

We forecast the expected cosmological constraints from a combination of probes of both the universal expansion rate and matter perturbation growth, in the form of weak lensing tomography, galaxy tomography, supernovae, and the cosmic microwave background incorporating all cross-correlations between the observables for an extensive cosmological parameter set. We allow for nonzero curvature and parameterize our ignorance of the early universe by allowing for a non-negligible fraction of dark energy (DE) at high redshifts. We find that early DE density can be constrained to 0. 2% of the critical density of the universe with Planck combined with a ground-based LSST-like survey, while curvature can be constrained to 0. 06%. However, these additional degrees of freedom degrade our ability to measure late-time dark energy and the sum of neutrino masses. We find that the combination of cosmological probes can break degeneracies and constrain the sum of neutrino masses to 0. 04 eV, present DE density also to 0. 2% of the critical density, and the equation of state to 0. 01---roughly a factor of 2 degradation in the constraints overall compared to the case without allowing for early DE. The constraints for a space-based mission are similar. Even a modest 1% dark energy fraction of the critical density at high redshift, if not accounted for in future analyses, biases the cosmological parameters by up to 2. Our analysis suggests that throwing out nonlinear scales (multipoles >1000) may not result in significant degradation in future parameter measurements when multiple cosmological probes are combined. We find that including cross-correlations between the different probes can result in improved constraints by up to a factor of 2 for the sum of neutrino masses and early dark energy density.