  The effect of weak gravitational lensing on the cosmic microwave background
(CMB) temperature anisotropies and polarization will provide access to
cosmological information that cannot be obtained from the primary anisotropies
alone. We compare the information content of the lensed B-mode polarization
power spectrum, properly accounting for the non-Gaussian correlations between
the power on different scales, with that of the unlensed CMB fields and the
lensing potential. The latter represent the products of an (idealised) optimal
analysis that exploits the lens-induced non-Gaussianity to reconstruct the
fields. Compressing the non-Gaussian lensed CMB into power spectra is wasteful
and leaves a tight degeneracy between the equation of state of dark energy and
neutrino mass that is much stronger than in the more optimal analysis. Despite
this, a power spectrum analysis will be a useful first step in analysing future
B-mode polarization data. For this reason, we also consider how to extract
accurate parameter constraints from the lensed B-mode power spectrum. We show
with simulations that for cosmic-variance-limited measurements of the lensed
B-mode power, including the non-Gaussian correlations in existing likelihood
approximations gives biased parameter results. We develop a more refined
likelihood approximation that performs significantly better. This new
approximation should also be of more general interest in the wider context of
parameter estimation from Gaussian CMB data.
