Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings

Understand

The Planck mission has conclusively detected lensing of the Cosmic Microwave Background (CMB) radiation from foreground sources to an overall significance of greater than $25\sigma$.

• The high precision of this measurement motivates the development of a more complete formulation of the calculation of this effect.
• While most effects on the CMB anisotropies are widely studied through direct solutions of the Boltzmann equation, the non-linear effect of CMB lensing is formulated through the solutions of the geodesic equation.
• In this paper, we present a new formalism to the calculation of the lensing effect by \emph{directly solving the Boltzmann equation}, as we did in the calculation of the CMB anisotropies at recombination.