  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 arcminutes (50 < l < 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 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 three due to their complementarity. For the
dark energy parameterization w(a) = w0 + wa(1-a), the marginalized errors from
lensing alone are sigma(w0) = 0.03 fsky^{-1/2} and sigma(wa) = 0.1 fsky^{-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 hyper-extended perturbation theory to compute the nonlinear
lensing bispectrum for dark energy models. Accurate model predictions of the
bispectrum in the moderately nonlinear 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.
