Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations

Andrei Lazanu, Tommaso Giannantonio, Marcel Schmittfull, and E. P. S. Shellard
Phys. Rev. D 93, 083517 – Published 20 April 2016

Abstract

We study the matter bispectrum of the large-scale structure by comparing different perturbative and phenomenological models with measurements from N-body simulations obtained with a modal bispectrum estimator. Using shape and amplitude correlators, we directly compare simulated data with theoretical models over the full three-dimensional domain of the bispectrum, for different redshifts and scales. We review and investigate the main perturbative methods in the literature that predict the one-loop bispectrum: standard perturbation theory, effective field theory, resummed Lagrangian and renormalized perturbation theory, calculating the latter also at two loops for some triangle configurations. We find that effective field theory (EFT) succeeds in extending the range of validity furthest into the mildly nonlinear regime, albeit at the price of free extra parameters requiring calibration on simulations: EFT is found to be accurate to 5% up to a scale of kmax*0.4h/Mpc at z=1, compared with kmax*0.2h/Mpc at z=1 for most other one-loop perturbative methods. For the more phenomenological halo model, we confirm that despite its validity in the deeply nonlinear regime it has a deficit of power on intermediate scales, which worsens at higher redshifts (the maximum deficit in the amplitude correlator is 20% at z=1, and up to 40% at z=2); this issue is ameliorated, but not solved, by combined halo-perturbative models. We show from simulations that in this transition region there is a strong squeezed bispectrum component that is significantly underestimated in the halo model at earlier redshifts. We thus propose a phenomenological method for alleviating this deficit, which we develop into a simple phenomenological “three-shape” benchmark model based on the three fundamental shapes we have obtained from studying the halo model. When calibrated on the simulations, this three-shape benchmark model accurately describes the bispectrum on all scales and redshifts considered, providing a prototype bispectrum Halofit-like methodology that could be used to describe and test parameter dependencies.

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  • Received 18 November 2015

DOI:https://doi.org/10.1103/PhysRevD.93.083517

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Andrei Lazanu1,*, Tommaso Giannantonio2,1,†, Marcel Schmittfull3,‡, and E. P. S. Shellard1,§

  • 1Centre for Theoretical Cosmology, DAMTP, University of Cambridge, CB3 0WA, United Kingdom
  • 2Kavli Institute for Cosmology Cambridge, Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom
  • 3Berkeley Center for Cosmological Physics, Department of Physics and Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, USA

  • *A.Lazanu@damtp.cam.ac.uk
  • T.Giannantonio@ast.cam.ac.uk
  • M.Schmittfull@berkeley.edu
  • §E.P.S.Shellard@damtp.cam.ac.uk

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Vol. 93, Iss. 8 — 15 April 2016

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