Unified approach to secondary effects on the CMB B-mode polarization

Understand

We develop a systematic and unified approach to estimate all possible secondary (i.e.

• non-primordial) nonlinear effects to the cosmic microwave background (CMB) polarization, named curve-of-sight integration approach.
• In this approach, the Boltzmann equation for polarized photons is rewritten in a line-of-sight integral along an exact geodesic in the perturbed universe, rather than a geodesic in the background universe used in the linear-order CMB calculation.
• This approach resolves the difficulty to solve the Boltzmann hierarchy with the nonlinear gravitational effects in the photon free-streaming regime and thus unifies the standard remapping approach for CMB lensing into the direct approach solving the Boltzmann equation for the nonlinear collisional effects.