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SUMMARY:Flat-sky angular power spectrum revisited - Zucheng Gao
DTSTART:20230503T121500Z
DTEND:20230503T124000Z
UID:TALK200533@talks.cam.ac.uk
CONTACT:Hannah Uebler
DESCRIPTION:We revisit the flat-sky approximation for evaluating the angul
 ar power spectra of projected random fields by retaining information about
  the correlations along the line of sight. For the case of projections wit
 h broad\, overlapping radial window functions\, these line-of-sight correl
 ations are suppressed and are ignored in the commonly adopted Limber appro
 ximation. However\, retaining the correlations is important for narrow win
 dow functions or unequal-time spectra but introduces significant computati
 onal difficulties due to the highly oscillatory nature of the integrands i
 nvolved. We deal with the integral over line-of-sight wave-modes in the fl
 at-sky approximation analytically\, using the FFTlog expansion of the 3D p
 ower spectrum. This results in an efficient computational method with a pe
 rformance time comparable to the Limber approximation\, which is a substan
 tial improvement compared to any full-sky approaches. We apply our results
  to galaxy clustering (with and without redshift-space distortions) and CM
 B lensing observables in a flat \nΛCDM universe. In the case of galaxy cl
 ustering\, we find excellent agreement with the full-sky results on large 
 (percent-level agreement) and intermediate (subpercent agreement) scales\,
  dramatically outperforming the Limber approximation for both wide and nar
 row window functions\, and in equal- and unequal-time cases. In the case o
 f CMB lensing\, the flat-sky approach yields subpercent agreement for mult
 ipoles ℓ ≳ 20 with discrepancies gradually increasing to tens of perce
 nt at smaller ℓ. We further analyse these angular power spectra by isola
 ting the projection effects due to the observable and survey-specific wind
 ow functions\, separating them from the effects due to integration along t
 he line of sight and unequal-time mixing in the 3D power spectrum. All of 
 the angular power spectrum results presented in this paper are obtained us
 ing a Python code implementation\, which we make publicly available.
LOCATION:The Hoyle Lecture Theatre + Zoom 
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