Abstract
Abstract
We revisit the flat-sky approximation for evaluating the angular power spectra of
projected random fields by retaining information about the correlations along the line of
sight. For the case of projections with broad, overlapping radial window functions, these
line-of-sight correlations are suppressed and are ignored in the commonly adopted Limber
approximation. However, retaining the correlations is important for narrow window functions or
unequal-time spectra but introduces significant computational difficulties due to the highly
oscillatory nature of the integrands involved. We deal with the integral over line-of-sight
wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power
spectrum. This results in an efficient computational method, which is a substantial improvement
compared to any full-sky approaches. We apply our results to galaxy clustering (with and without
redshift-space distortions), CMB lensing and galaxy lensing observables in a flat
ΛCDM universe. In the case of galaxy clustering, we find excellent agreement with
the full-sky results on large (percent-level agreement) and intermediate or small (subpercent
agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow
window functions, and in equal- and unequal-time cases. In the cases of lensing, we show on the
full-sky that the angular power spectrum of the lensing convergence can be very well approximated
by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational
potential, even on large scales. Combining this approximation with our flat-sky techniques
provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all
scales. We further analyse the clustering and lensing angular power spectra by isolating the
projection effects due to the observable- and survey-specific window functions, separating them
from the effects due to integration along the 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
using a Python code implementation, which we make publicly available.
Subject
Astronomy and Astrophysics
Reference52 articles.
1. Cosmology and fundamental physics with the Euclid satellite;Amendola;Living Rev. Rel.,2018
2. The DESI Experiment Part I: Science,Targeting, and Survey Design;DESI Collaboration,2016
3. Large Synoptic Survey Telescope: Dark Energy Science Collaboration;LSST Dark Energy Science Collaboration,2012
4. Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report;Spergel,2015
5. Cosmology with the SPHEREX All-Sky Spectral Survey;SPHEREx Collaboration,2014