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Towards a non-Gaussian model of redshift space distortions

Cuesta-Lazaro, Carolina; Li, Baojiu; Eggemeier, Alexander; Zarrouk, Pauline; Baugh, Carlton M.; Nishimichi, Takahiro; Takada, Masahiro

Towards a non-Gaussian model of redshift space distortions Thumbnail


Carolina Cuesta-Lazaro

Alexander Eggemeier

Takahiro Nishimichi

Masahiro Takada


To understand the nature of the accelerated expansion of the Universe, we need to combine constraints on the expansion rate and growth of structure. The growth rate is usually extracted from 3D galaxy maps by exploiting the effects of peculiar motions on galaxy clustering. However, theoretical models of the probability distribution function (PDF) of galaxy pairwise peculiar velocities are not accurate enough on small scales to reduce the error on theoretical predictions to the level required to match the precision expected for measurements from future surveys. Here, we improve the modelling of the pairwise velocity distribution by using the Skew-T PDF, which has non-zero skewness and kurtosis. Our model accurately reproduces the redshift space multipoles (monopole, quadrupole, and hexadecapole) predicted by N-body simulations, above scales of about 10h−1Mpc⁠. We illustrate how a Taylor expansion of the streaming model can reveal the contributions of the different moments to the clustering multipoles, which are independent of the shape of the velocity PDF. The Taylor expansion explains why the Gaussian streaming model works well in predicting the first two redshift space multipoles, although the velocity PDF is non-Gaussian even on large scales. Indeed, any PDF with the correct first two moments would produce precise results for the monopole down to scales of about 10h−1Mpc⁠, and for the quadrupole down to about 30h−1Mpc⁠. An accurate model for the hexadecapole needs to include higher order moments.


Cuesta-Lazaro, C., Li, B., Eggemeier, A., Zarrouk, P., Baugh, C. M., Nishimichi, T., & Takada, M. (2020). Towards a non-Gaussian model of redshift space distortions. Monthly Notices of the Royal Astronomical Society, 498(1), 1175-1193.

Journal Article Type Article
Acceptance Date Jul 2, 2020
Online Publication Date Aug 6, 2020
Publication Date 2020-10
Deposit Date Feb 10, 2020
Publicly Available Date Oct 22, 2020
Journal Monthly Notices of the Royal Astronomical Society
Print ISSN 0035-8711
Electronic ISSN 1365-2966
Publisher Royal Astronomical Society
Peer Reviewed Peer Reviewed
Volume 498
Issue 1
Pages 1175-1193
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Published Journal Article (5.7 Mb)

Copyright Statement
This article has been accepted for publication in Monthly notices of the Royal Astronomical Society. ©: 2020 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.

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