Speaker
Description
Two-point correlation functions are among the most powerful probes of cosmology. Additional information is obtained from cross-correlations, which help mitigate systematic effects and break parameter degeneracies. Their numerical evaluation, however, is computationally demanding because it requires multi-dimensional integrations of highly oscillatory functions involving probe kernels and spherical Bessel functions.
The Limber approximation is commonly used to simplify these calculations, but its range of validity becomes limited for the accuracy and angular scales targeted by upcoming surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and the Euclid mission.
In this work we introduce UltraLevin, a Levin-type algorithm for oscillatory cosmological integrals that combines a reformulation of the Bessel integrals with a spectral ODE solver based on ultraspherical polynomials. The algorithm is designed to evaluate batches of multipoles simultaneously and to automatically identify the effective support of the probe kernels, reducing the computational cost of the integrations.
We validate the approach and compare its numerical accuracy and computational performance with existing implementations, including the non-Limber angular power spectrum calculation available in the Core Cosmology Library (CCL). We also identify the regimes where the Limber approximation remains valid for galaxy clustering, CMB lensing, and galaxy weak lensing.
The method is implemented in the Numerical Cosmology Library (NumCosmo), providing an efficient tool for precision cosmology analyses.