Toward Accurate Modeling of the Nonlinear Matter Bispectrum: Standard Perturbation Theory and Transients from Initial Conditions

Abstract

Accurate modeling of nonlinearities in the galaxy bispectrum, the Fourier transform of the galaxy three-point correlation function, is essential to fully exploit it as a cosmological probe. In this paper, we present numerical and theoretical challenges in modeling the nonlinear bispectrum. First, we test the robustness of the matter bispectrum measured from N-body simulations using different initial conditions generators. We run a suite of N-body simulations using the Zel'dovich approximation and second-order Lagrangian perturbation theory (2LPT) at different starting redshifts, and find that transients from initial decaying modes systematically reduce the nonlinearities in the matter bispectrum. To achieve 1% accuracy in the matter bispectrum for $z\le 3$ on scales $k<1$ $h$/Mpc, 2LPT initial conditions generator with initial redshift of $z\gtrsim 100$ is required. We then compare various analytical formulas and empirical fitting functions for modeling the nonlinear matter bispectrum, and discuss the regimes for which each is valid. We find that the next-to-leading order (one-loop) correction from standard perturbation theory matches with N-body results on quasi-linear scales for $z\ge 1$. We find that the fitting formula in Gil-Mar\'ın et al. (2012) accurately predicts the matter bispectrum for $z\le 1$ on a wide range of scales, but at higher redshifts, the fitting formula given in Scoccimarro & Couchman (2001) gives the best agreement with measurements from N-body simulations.

14 pages, 11 figures, submitted to MNRAS. V2: fixed an error in model predictions

References in corpus (7)

• Cosmological Constraints from the SDSS Luminous Red Galaxies
• Transients from Initial Conditions in Cosmological Simulations
• The bispectrum of galaxies from high-redshift galaxy surveys: primordial non-Gaussianity and non-linear galaxy bias
• Primordial non-Gaussianity, scale-dependent bias, and the bispectrum of galaxies
• The Effect of Large-Scale Structure on the SDSS Galaxy Three-Point Correlation Function
• Three-Point Correlation Functions of SDSS Galaxies: Luminosity and Color Dependence in Redshift and Projected Space
• Lagrangian perturbations and the matter bispectrum II: the resummed one-loop correction to the matter bispectrum

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