Improved cosmic microwave background (de-)lensing using general spherical harmonic transforms

TL;DR

This paper introduces an optimized numerical code utilizing nonuniform fast Fourier transforms for efficient and accurate lensing and delensing operations on the sphere, significantly benefiting future cosmic microwave background experiments.

Contribution

The authors present a highly efficient, accurate, and publicly available code for spherical harmonic transforms that outperforms existing software and simplifies lensing and delensing computations.

Findings

Code achieves high-resolution, accurate maps within seconds on a laptop.

Performs both lensing and its adjoint efficiently, eliminating the need for inverse deflection fields.

Outperforms current software by a wide margin in speed and accuracy.

Abstract

Deep cosmic microwave background polarization experiments allow a very precise internal reconstruction of the gravitational lensing signal in pricinple. For this aim, likelihood-based or Bayesian methods are typically necessary, where very large numbers of lensing and delensing remappings on the sphere are sometimes required before satisfactory convergence. We discuss here an optimized piece of numerical code in some detail that is able to efficiently perform both the lensing operation and its adjoint (closely related to delensing) to arbitrary accuracy, using nonuniform fast Fourier transform technology. Where applicable, we find that the code outperforms current widespread software by a very wide margin. It is able to produce high-resolution maps that are accurate enough for next-generation cosmic microwave background experiments on the timescale of seconds on a modern laptop. The adjoint operation performs similarly well and removes the need for the computation of inverse deflection fields. This publicly available code enables de facto efficient spherical harmonic transforms on completely arbitrary grids, and it might be applied in other areas as well.