New operator approach to the CMB aberration kernels in harmonic space

Understand

Aberration kernels describe how harmonic-space multipole coefficients of cosmic microwave background (CMB) observables transform under Lorentz boosts of the reference frame.

• For spin-weighted CMB observables, transforming like the CMB temperature (i.e.
• Doppler weight $d = 1$), we show that the aberration kernels are the matrix elements of a unitary boost operator in harmonic space.
• Algebraic properties of the rotation and boost generators then give simple, exact recursion relations that allow us to raise or lower the multipole quantum numbers $\ell$ and $m$, and the spin weight $s$.