Complex evaluation of angular power spectra: Going beyond the Limber approximation

Understand

Angular power spectra are central to the study of our Universe.

• In this paper, I develop a new method for the numeric evaluation and analytic estimation of the angular cross-power spectrum of two random fields using complex analysis and Picard- Lefschetz theory.
• The proposed continuous deformation of the integration domain resums the highly oscillatory integral into a convex integral whose integrand decays exponentially.
• This deformed integral can be quickly evaluated with conventional integration techniques.