Lensing simulations by Taylor expansion -- not so inefficient after all

TL;DR

This paper demonstrates that Taylor expansion-based CMB lensing simulations, previously thought inefficient, can be effective on the full sky with proper generalization, offering a competitive alternative to existing methods.

Contribution

The authors extend the flat-sky Taylor lensing method to the full sky and benchmark its performance against Lenspix, showing it is a viable and efficient alternative.

Findings

The generalized Taylor method is feasible for full-sky CMB lensing simulations.

It achieves 1/3 to 2/3 the speed of Lenspix with comparable accuracy.

The method's performance is limited by spherical harmonic transform speeds.

Abstract

Cosmic Microwave Background lensing simulation by Taylor expansion has long been considered impractical due to slow convergence, but a recent flat-sky implementation shows that a simple trick eliminates this problem, making Taylor lensing a fast and simple lensing algorithm for the flat sky. Here we generalize the method to the full sky, and study its convergence and performance relative to a commonly used numerical code, Lenspix, with extensive benchmarks of both. Compared to the flat sky case, the method takes a speed hit due to the slow speed of spherical harmonic transforms compared to fast Fourier transforms, resulting in speeds of 1/3 to 2/3 of Lenspix for similar accuracy.