  Gravitational lensing of the Cosmic Microwave Background (CMB) encodes
cosmological information in the observed anisotropies of temperature and
polarization. Accurate extraction of this additional information requires
precise modeling of the covariance matrix of the power spectra of observed CMB
fields. We introduce a new analytical model to describe the non-Gaussian
structure of this covariance matrix and display the importance of second-order
terms that were previously neglected. When compared with direct numerical
simulations our model captures parameter errors to better than a few percent
for cases where the non-Gaussianity causes an order unity degradation in
errors. We also provide a detailed comparison between the information content
of lensed CMB power spectra and ideal reconstruction of the lensing potential.
We illustrate the impact of the non-Gaussian terms in the power spectrum
covariance by providing Fisher errors on the sum of the masses of the
neutrinos, the dark energy equation of state, and the curvature of the
Universe.
