Beyond Limber: Efficient computation of angular power spectra for galaxy clustering and weak lensing

Xiao Fang, Elisabeth Krause, Tim Eifler, Niall MacCrann

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Angular two-point statistics of large-scale structure observables are important cosmological probes. To reach the high accuracy required by the statistical precision of future surveys, some of these statistics may need to be computed without the commonly employed Limber approximation; the exact computation however requires integration over Bessel functions, and a brute-force evaluation is slow to converge. We present a new method based on our generalized FFTLog algorithm for the efficient computation of angular power spectra beyond the Limber approximation. The new method significantly simplifies the calculation and improves the numerical speed and stability. It is easily extended to handle integrals involving derivatives of Bessel functions, making it equally applicable to numerically more challenging cases such as contributions from redshift-space distortions and Doppler effects. We implement our method for galaxy clustering and galaxy-galaxy lensing power spectra. We find that using the Limber approximation for galaxy clustering in future analyses like LSST Year 1 and DES Year 6 may cause significant biases in cosmological parameters, indicating that going beyond the Limber approximation is necessary for these analyses.

Original languageEnglish (US)
Article number010
JournalJournal of Cosmology and Astroparticle Physics
Issue number5
StatePublished - May 2020


  • cosmological parameters from LSS
  • dark energy experiments
  • galaxy clustering
  • weak gravitational lensing

ASJC Scopus subject areas

  • Astronomy and Astrophysics


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