Probing decisive answers to dark energy questions from cosmic   complementarity and lensing tomography
  We study future constraints on dark energy parameters determined from several combinations of CMB experiments, supernova data, and weak lensing surveys with and without tomography. In this analysis, we look in particular for combinations that will bring the uncertainties to a level of precision tight enough (a few percent) to answer decisively some of the dark energy questions. We probe the dark energy using two variants of its equation of state, and its energy density.We consider a set of 13 cosmological and systematic parameters, and assume reasonable priors on the lensing and supernova systematics. We consider various lensing surveys: a wide survey with f_{sky}=0.7, and with 2 (WLT2) and 5 (WLT5) tomographic bins; a deep survey with 10 bins (WLT10). The constraints found from Planck, 2000 supernovae with z_max=0.8, and WLT2 are: {sigma(w_0)=0.086, sigma(w_1)=0.069}, {sigma(w_0)=0.088, sigma(w_a)=0.11}, and {sigma(E_1)=0.029, sigma(E_2)=0.065}. With 5 bins, we find {sigma(w_0)=0.04, sigma(w_1)=0.034}, {sigma(w_0)=0.041, sigma(w_a)=0.056}, and {sigma(E_1)=0.012, sigma(E_2)=0.049}. Finally, we find from Planck, 2000 supernovae with z_max=1.5, and WLT10 with f_{sky}=0.1: {sigma(w_0)=0.032, sigma(w_1)=0.027}, {sigma(w_0)=0.033, sigma(w_a)=0.040}, and {sigma(E_1)=0.01, sigma(E_2)=0.04}. Although some worries remain about other systematics, our study shows that after the combination of the 3 probes, lensing tomography with many redshift bins and large coverages of the sky has the potential to add key improvements to the dark energy parameter constraints. However, the requirement for very ambitious and sophisticated surveys in order to achieve some of the constraints or to improve them suggests the need for new tests to probe the nature of dark energy in addition to constraining its equation of state. (Abriged) 
Mustapha Ishak (Princeton University)