Fast CMB lensing using statistical interpolation on the sphere

TL;DR

The paper introduces FLINTS, a fast and accurate pixel-based interpolation method on the sphere, enabling precise and efficient computation of lensed CMB maps with minimal error, suitable for high-resolution cosmological analyses.

Contribution

It presents FLINTS, a novel interpolation technique that improves accuracy and speed for spherical field interpolation, specifically applied to CMB lensing simulations.

Findings

Achieves 0.02% precision at Nside=4096 in CMB map simulations.

Lensed power spectra are accurate within 0.5% up to l=3000.

Outperforms existing methods by 2-3 orders of magnitude in precision for the same computational cost.

Abstract

We describe a accurate and fast pixel-based statistical method to interpolate fields of arbitrary spin on the sphere. We call this method Fast and Lean Interpolation on the Sphere (FLINTS). The method predicts the optimal interpolated values based on the theory of isotropic Gaussian random fields and provides an accurate error estimate at no additional cost. We use this method to compute lensed Cosmic Microwave Background (CMB) maps precisely and quickly, achieving a relative precision of 0.02% at a HEALPix resolution of Nside=4096, for a bandlimit of l_max=4096 in the same time it takes to simulate the original, unlensed CMB map. The method is suitable for efficient, distributed memory parallelization. The power spectra of our lensed maps are accurate to better than 0.5% at l=3000 for the temperature, the E and B mode of the polarization. As expected theoretically, we demonstrate that, on realistic cases, this method is between two to three orders of magnitude more precise than other known interpolation methods for the same computational cost.