CMB Delensing Beyond the B Modes

Gravitational lensing by large-scale structure significantly impacts observations of the cosmic microwave background (CMB): it smooths the acoustic peaks in temperature and $E$-mode polarization power spectra, correlating previously uncorrelated modes; and it converts $E$-mode polarization into $B$-mode polarization. The act of measuring and removing the effect of lensing from CMB maps, or delensing, has been well studied in the context of $B$ modes, but little attention has been given to the delensing of the temperature and $E$ modes. In this paper, we model the expected delensed $T$ and $E$ power spectra to all orders in the lensing potential, demonstrating the sharpening of the acoustic peaks and a significant reduction in lens-induced power spectrum covariances. We then perform cosmological forecasts, demonstrating that delensing will yield improved sensitivity to parameters with upcoming surveys. We highlight the breaking of the degeneracy between the effective number of neutrino species and primordial helium fraction as a concrete application. We also show that delensing increases cosmological information as long as the measured lensing reconstruction is included in the analysis. We conclude that with future data, delensing will be crucial not only for primordial $B$-mode science but for a range of other observables as well.