Description
Weak gravitational lensing has become an increasingly powerful probe for constraining cosmological parameters and exploring the nature of dark matter and dark energy. Stage-IV cosmological analyses will require rapid computation of summary statistics across wide angular scales and multiple tomographic bins to enable efficient sampling of high-dimensional parameter spaces.
In this talk, I will present a novel mathematical framework that accelerates cosmological inference by reformulating multi-layer numerical integrals into efficient tensor operations. This approach approximates key physical quantities—including the matter power spectra, kernel functions, and scale factors—as piecewise linear functions of comoving distance. Consequently, each segment of the line-of-sight integral can be solved analytically, yielding a compact expression for the lensing angular power spectra.
The resulting formalism expresses the power spectra as a sum over a cosmology-dependent coefficient tensor, with quadratic dependence on nuisance parameters such as tomographic redshift distributions. We validate our method by demonstrating sub-percent level accuracy compared to the Core Cosmology Library (CCL; Chisari et al. 2019), and report a two-fold improvement in computational speed under the Stage-IV survey conditions. Further acceleration is achieved using the JAX library, enabling automatic differentiation over cosmological parameters and efficient parallelisation via CPU and GPU support.
This work lays the foundation for a new class of fast, scalable cosmological inference tools—facilitating analytic marginalisation over nuisance parameters, accurate modelling of angular power spectra in curved spacetime, extensions beyond the Limber approximation, and accelerated computation of higher-order lensing statistics—making it well suited for next-generation cosmological surveys.
