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 non-zero 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 two 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 \sigma .
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 .