Flat-sky angular power spectra revisited

Gao, Zucheng; Vlah, Zvonimir; Challinor, Anthony (2024) Flat-sky angular power spectra revisited. Journal of Cosmology and Astroparticle Physics, 2024 (02). ISSN 1475-7516

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Abstract

We revisit the flat-sky approximation for evaluating the angular power spectra ofprojected random fields by retaining information about the correlations along the line ofsight. For the case of projections with broad, overlapping radial window functions, theseline-of-sight correlations are suppressed and are ignored in the commonly adopted Limberapproximation. However, retaining the correlations is important for narrow window functions orunequal-time spectra but introduces significant computational difficulties due to the highlyoscillatory nature of the integrands involved. We deal with the integral over line-of-sightwave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D powerspectrum. This results in an efficient computational method, which is a substantial improvementcompared to any full-sky approaches. We apply our results to galaxy clustering (with and withoutredshift-space distortions), CMB lensing and galaxy lensing observables in a flatΛCDM universe. In the case of galaxy clustering, we find excellent agreement withthe full-sky results on large (percent-level agreement) and intermediate or small (subpercentagreement) scales, dramatically out-performing the Limber approximation for both wide and narrowwindow functions, and in equal- and unequal-time cases. In the cases of lensing, we show on thefull-sky that the angular power spectrum of the lensing convergence can be very well approximatedby projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitationalpotential, even on large scales. Combining this approximation with our flat-sky techniquesprovides an efficient and accurate evaluation of the CMB lensing angular power spectrum on allscales. We further analyse the clustering and lensing angular power spectra by isolating theprojection effects due to the observable- and survey-specific window functions, separating themfrom the effects due to integration along the line of sight and unequal-time mixing in the 3Dpower spectrum. All of the angular power spectrum results presented in this paper are obtainedusing a Python code implementation, which we make publicly available.

Item Type:	Article
Uncontrolled Keywords:	large-scale structure; angular power spectrum
Subjects:	NATURAL SCIENCES > Physics > Astronomy and Astrophysics
Divisions:	Theoretical Physics Division
Depositing User:	Zvonimir Vlah
Date Deposited:	15 Jan 2025 07:33
URI:	http://fulir.irb.hr/id/eprint/9440
DOI:	10.1088/1475-7516/2024/02/003

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