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2008

Extended Limber Approximation

LoVerde, Marilena, Afshordi, Niayesh

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We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in 1/(\ell+1/2).

This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large \ell's.
We show that the error in ordinary Limber approximation is O(1/\ell^2).
We also provide a simple expression for the second order correction to the Limber formula, which improves the accuracy to O(1/\ell^4).

Extended Limber Approximation · Around

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D. N. Limber, ApJ 117
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N. Kaiser, ApJ 388
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N. Kaiser, ApJ 498
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D. J. Eisenstein and W. Hu, ApJ 496
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W. Hu, Phys. Rev. D 62
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