Cosmological parameters from lensing power spectrum and bispectrum tomography

We examine how lensing tomography with the bispectrum and power spectrum can constrain cosmological parameters and the equation of state of dark energy. Our analysis uses the full information at the two- and three-point level from angular scales of a few degrees to 5 arcmin (50 less than or equal to l less than or equal to 3000), which will be probed by lensing surveys. We use all triangle configurations, cross-power spectra and bispectra constructed from up to three redshift bins with photometric redshifts, and all relevant covariances in our analysis. We find that the parameter constraints from bispectrum tomography are comparable to those from power spectrum tomography. Combining the two improves parameter accuracies by a factor of 3 due to their complementarity. For the dark energy parametrization w(a) = w(0) + w(a)(l - a), the marginalized errors from lensing alone are sigma(w(0)) similar to 0.03f(sky)(-1/2) and sigma(w(a)) similar to 0.1f(sky)(-1/2). We show that these constraints can be further improved when combined with measurements of the cosmic microwave background or Type Ia supernovae. The amplitude and shape of the mass power spectrum are also shown to be precisely constrained. We use hyperextended perturbation theory to compute the non-linear lensing bispectrum for dark energy models. Accurate model predictions of the bispectrum in the moderately non-linear regime, calibrated with numerical simulations, will be needed to realize the parameter accuracy we have estimated. Finally, we estimate how well the lensing bispectrum can constrain a model with primordial non-Gaussianity.