Information content of the lensed CMB power spectra

Weak lensing of the cosmic microwave background (CMB) is expected to be detected with the next generation of observations. We review recent theoretical refinements in the calculation of the lensed spectra and discuss the extent to which these corrections are required to avoid parameter biases from future data. For a future satellite mission (with ∼1 μK′ sensitivity), targeting large-angle B modes from gravitational waves, the flat-sky and gradient approximations must be dropped and non-linear matter clustering included if r is near the detection threshold (r ∼ 2 × 10−4). We also discuss the role of the lensed CMB spectra in constraining cosmological parameters, such as light neutrino masses and the dark energy model, that are essentially degenerate with respect to the primary CMB fluctuations. Non-Gaussianities and degeneracies limit what can be learned from the lensed spectra, but a simple power spectrum analysis will still be a worthwhile first step. Analysing futuristic, cosmic-variance-limited lensed B-mode spectra requires careful attention to the choice of likelihood approximation. We show that approximations in current use for the analysis of Gaussian fields produce biased results on lensed simulations. We highlight a more refined approximation that performs significantly better.