Kavli Affiliate: Anthony Challinor
| First 5 Authors: Zucheng Gao, Zvonimir Vlah, Anthony Challinor, ,
| Summary:
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. With broad, overlapping radial window
functions, these line-of-sight correlations are suppressed and are ignored in
the 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. For 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 case of lensing, we
show on the full sky that the angular power spectrum of the 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.
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