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Cited by 437

The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.

Extended Limber approximation

Open access
LoVerde, Marilena, Afshordi, Niayesh·2008·Physical Review D
DOI 10.1103/physrevd.78.123506
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Abstract

We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in $(\ensuremath{\ell}+1/2{)}^{\ensuremath{-}1}$. This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large $\ensuremath{\ell}$'s. We show that the error in ordinary Limber approximation is $\mathcal{O}({\ensuremath{\ell}}^{\ensuremath{-}2})$. We also provide a simple expression for the 2nd order correction to the Limber formula, which improves the accuracy to $\mathcal{O}({\ensuremath{\ell}}^{\ensuremath{-}4})$. This correction can be especially useful for narrow redshift bins, or samples with small redshift overlap, for which the 0th order Limber formula has a large error. We also point out that using $\ensuremath{\ell}$ instead of $\ensuremath{\ell}+1/2$, as is often done in the literature, spoils the accuracy of the approximation to $\mathcal{O}({\ensuremath{\ell}}^{\ensuremath{-}1})$.

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Metadata

Authors
LoVerde, M., & Afshordi, N.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2008-12-03
Volume
78
Issue
12
ISSN
  • 0556-2821 (ISSN-L)
  • 1550-7998
  • 1550-2368
DOI
10.1103/physrevd.78.123506
OpenAlex
W2115324751
Cited by
437
References
13
FWCI
4.91
Type
journal article
Language
en
Open access
green

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CoChat. (2026). Citation check: Extended Limber approximation. https://app.cochat.ai/papers/10.1103/physrevd.78.123506
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LoVerde, M., & Afshordi, N. (2008). Extended Limber approximation. Physical Review D. https://doi.org/10.1103/physrevd.78.123506

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