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 cosmic microwave background experiments, supernova data, and cosmic-shear surveys with and without tomography. In this analysis, we look in particular for combinations of experiments that will bring the uncertainties to a level of precision tight enough ( a few per cent) to answer decisively some of the questions regarding dark energy. In view of the parametrization dependence problems, we probe the dark energy using two variants of its equation of state w( z), and its energy density rho de( z). For the latter, we model rho de( z) as a continuous function interpolated using dimensionless parameters epsilon i(zi) = rho de(zi)/rho de(0). We consider a large set of 13 cosmological and systematic parameters, and assume reasonable priors on the lensing and supernova systematics. For the CMB, we consider future constraints from eight years of data from WMAP, one year of data from Planck, and one year of data from the Atacama Cosmology Telescope ( ACT). We use two sets of 2000 supernovae with z(max) = 0.8 and 1.5 respectively, and consider various cosmic- shear reference surveys: a wide ground- based- like survey, covering 70 per cent of the sky, and with successively two and five tomographic bins; and a deep- space- based- like survey with 10 tomographic bins and various sky coverages. The 1 sigma constraints found are {sigma(w(0)) = 0.086, sigma(w(1)) = 0.069}, {sigma(w(0)) = 0.088, sigma(w(a)) = 0.11}, and {sigma(epsilon(1)) = 0.029, sigma(epsilon(2)) = 0.065} from Planck, supernovae and the ground-based-like lensing survey with two bins. When five bins are used within the same combination the constraints reduce to {sigma(w(0)) = 0.04, sigma(w(1)) = 0.034}, {sigma(w(0)) = 0.041, sigma(w(a)) = 0.056}, and {sigma(epsilon(1)) = 0.012, sigma(epsilon(2)) = 0.049}. Finally, when the deep lensing survey with 10 per cent coverage of the sky and 10 tomographic bins is used along with Planck and the deep supernova survey, the constraints reduce to {sigma(w(0)) = 0.032, sigma(w(1)) = 0.027}, {sigma(w(0)) = 0.033, sigma(w(a)) = 0.04}, and {sigma(epsilon(1)) = 0.01, sigma(epsilon(2)) = 0.04}. Other coverages of the sky and other combinations of experiments are explored as well. Although some worries remain about other systematics, our study shows that, after the combination of the three 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 fact that very ambitious and sophisticated surveys are required in order to achieve some of these 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.